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Numerical Analysis and Computation Commons™

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Articles 31 - 60 of 236

Full-Text Articles in Numerical Analysis and Computation

(R1504) Second-Order Modified Nonstandard Runge-Kutta And Theta Methods For One-Dimensional Autonomous Differential Equations, Madhu Gupta, John M. Slezak, Fawaz K. Alalhareth, Souvik Roy, Hristo V. Kojouharov Dec 2021

(R1504) Second-Order Modified Nonstandard Runge-Kutta And Theta Methods For One-Dimensional Autonomous Differential Equations, Madhu Gupta, John M. Slezak, Fawaz K. Alalhareth, Souvik Roy, Hristo V. Kojouharov

Applications and Applied Mathematics: An International Journal (AAM)

Nonstandard finite difference methods (NSFD) are used in physical sciences to approximate solutions of ordinary differential equations whose analytical solution cannot be computed. Traditional NSFD methods are elementary stable but usually only have first order accuracy. In this paper, we introduce two new classes of numerical methods that are of second order accuracy and elementary stable. The methods are modified versions of the nonstandard two-stage explicit Runge-Kutta methods and the nonstandard one-stage theta methods with a specific form of the nonstandard denominator function. Theoretical analysis of the stability and accuracy of both modified NSFD methods is presented. Numerical simulations that …

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(R1458) A New Finite Difference Scheme For High-Dimensional Heat Equation, Jafar Biazar, Roxana Asayesh Dec 2021

(R1458) A New Finite Difference Scheme For High-Dimensional Heat Equation, Jafar Biazar, Roxana Asayesh

Applications and Applied Mathematics: An International Journal (AAM)

In this research‎, ‎a new second-order finite difference scheme is proposed to solve two and three- dimensional heat equation‎. Finite difference equations are determined via a discretization approach in which spatial second order partial derivatives in x and y directions are approximated simultaneously‎ while in the classic method, each spatial partial derivative is replaced by a central finite difference approximation, separately. By this new discretization scheme and also using the forward difference to the first-order time derivative, a finite difference equation is obtained for the parabolic equation. This approach is explicit and similar to other explicit approaches, an interval for …

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A High Order Finite Difference Method To Solve The Steady State Navier-Stokes Equations, Nihal J. Siriwardana, Saroj P. Pradhan Jun 2021

A High Order Finite Difference Method To Solve The Steady State Navier-Stokes Equations, Nihal J. Siriwardana, Saroj P. Pradhan

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we develop a fourth order finite difference method to solve the system of steady state Navier-Stokes equations and apply it to the benchmark problem known as the square cavity flow problem. The numerical results of 𝑢-velocity components and 𝑣-velocity components obtained at the center of the cavity are compared with the results obtained by the method developed by Greenspan and Casulli to solve the time dependent system of Navier-Stokes equations. The method described in this article is easy to implement and it has been shown to be more efficient and stable than the method by Greenspan and …

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Thermal-Diffusion And Diffusion-Thermo Effects On Heat And Mass Transfer In Chemically Reacting Mhd Casson Nanofluid With Viscous Dissipation, Timothy L. Oyekunle, Mojeed T. Akolade, Samson A. Agunbiade Jun 2021

Thermal-Diffusion And Diffusion-Thermo Effects On Heat And Mass Transfer In Chemically Reacting Mhd Casson Nanofluid With Viscous Dissipation, Timothy L. Oyekunle, Mojeed T. Akolade, Samson A. Agunbiade

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we examined the combined effects of dissipation and chemical reaction in Casson nanofluid motion through a vertical porous plate subjected to the magnetic field effect placed perpendicular to the flow channel. The physical problem is modeled using partial differential equations (PDEs). These sets of PDEs, with suitable similarity transformations, are simplified into ordinary differential equations (ODEs). Collocation technique with legendary basis function is utilized in solving the transformed equations. The numerical analysis on velocity, concentration, and temperature are plotted and tabled for different flow parameters. Our findings show that by raising the Casson parameter close to infinity, …

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Two Temperature Dual-Phase-Lag Fractional Thermal Investigation Of Heat Flow Inside A Uniform Rod, Vinayak Kulkarni, Gaurav Mittal Jun 2021

Two Temperature Dual-Phase-Lag Fractional Thermal Investigation Of Heat Flow Inside A Uniform Rod, Vinayak Kulkarni, Gaurav Mittal

Applications and Applied Mathematics: An International Journal (AAM)

A non-classical, coupled, fractionally ordered, dual-phase-lag (DPL) heat conduction model has been presented in the framework of the two-temperature theory in the bounded Cartesian domain. Due to the application of two-temperature theory, the governing heat conduction equation is well-posed and satisfying the required stability criterion prescribed for a DPL model. The mathematical formulation has been applied to a uniform rod of finite length with traction free ends considered in a perfectly thermoelastic homogeneous isotropic medium. The initial end of the rod has been exposed to the convective heat flux and energy dissipated by convection into the surrounding medium through the …

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Generation And Statistical Properties For Lindley-Polynomial Distribution, Dariush Ghorbanzadeh Jun 2021

Generation And Statistical Properties For Lindley-Polynomial Distribution, Dariush Ghorbanzadeh

Applications and Applied Mathematics: An International Journal (AAM)

For the modeling of the wind speed, we propose a family of distributions in polynomial form generating the Lindley distribution. We call this distribution Lindley-Polynomial distribution. The estimation of parameters using the maximum product spacing estimation method. A real data set has been considered to illustrate the practical utility of the paper.

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Hybrid Algorithm For Singularly Perturbed Delay Parabolic Partial Differential Equations, Imiru T. Daba, Gemechis F. Duressa Jun 2021

Hybrid Algorithm For Singularly Perturbed Delay Parabolic Partial Differential Equations, Imiru T. Daba, Gemechis F. Duressa

Applications and Applied Mathematics: An International Journal (AAM)

This study aims at constructing a numerical scheme for solving singularly perturbed parabolic delay differential equations. Taylor’s series expansion is applied to approximate the shift term. The obtained result is approximated by using the implicit Euler method in the temporal discretization on a uniform step size with the hybrid numerical scheme consisting of the midpoint upwind method in the outer layer region and the cubic spline method in the inner layer region on a piecewise uniform Shishkin mesh in the spatial discretization. The constructed scheme is an ε−uniformly convergent accuracy of order one. Some test examples are considered to testify …

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Replenishment Policy For Pareto Type Deteriorating Items With Quadratic Demand Under Partial Backlogging And Delay In Payments, Ganesh Kumar, Ramesh Inaniyan, Sunita - Dec 2020

Replenishment Policy For Pareto Type Deteriorating Items With Quadratic Demand Under Partial Backlogging And Delay In Payments, Ganesh Kumar, Ramesh Inaniyan, Sunita -

Applications and Applied Mathematics: An International Journal (AAM)

The present model develops a replenishment policy in which the demand rate is quadratic polynomial-time function. Deterioration rate is a Pareto type function. Shortages are partial backlogging and delay in payments are allowed. Holding cost is a linear function of time. The backlogging rate varies with the waiting duration for the next replenishment. The present paper determines the optimal policy for the individual by minimizing the total cost. The optimization procedure has been explained by a numerical example and a detailed sensitivity analysis of the optimal solution has been carried out to display the effect of various parameters.

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Impatient Customers In An Markovian Queue With Bernoulli Schedule Working Vacation Interruption And Setup Time, P. Manoharan, T. Jeeva Dec 2020

Impatient Customers In An Markovian Queue With Bernoulli Schedule Working Vacation Interruption And Setup Time, P. Manoharan, T. Jeeva

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, using probability generating function method, Impatient customers in an Markovian queue with Bernoulli schedule working vacation interruption and setup time is discussed. Customers impatience is due to the servers vacation. During the working vacation period, if there are customers in the queue, the vacation can be interrupted at a service completion instant and the server begins a regular service period with probability (1 - b) or continues the vacation with probability b. We obtain the probability generating functions of the stationary state probabilities, performance measures, sojourn time of a customer and stochastic decomposition of the queue length, …

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On A Multiserver Queueing System With Customers’ Impatience Until The End Of Service Under Single And Multiple Vacation Policies, Mokhtar Kadi, Amina A. Bouchentouf, Lahcene Yahiaoui Dec 2020

On A Multiserver Queueing System With Customers’ Impatience Until The End Of Service Under Single And Multiple Vacation Policies, Mokhtar Kadi, Amina A. Bouchentouf, Lahcene Yahiaoui

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with a multiserver queueing system with Bernoulli feedback and impatient customers (balking and reneging) under synchronous multiple and single vacation policies. Reneged customers may be retained in the system. Using probability generating functions (PGFs) technique, we formally obtain the steady-state solution of the proposed queueing system. Further, important performance measures and cost model are derived. Finally, numerical examples are presented.

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Accurate Spectral Algorithms For Solving Variable-Order Fractional Percolation Equations, M. A. Abdelkawy Dec 2020

Accurate Spectral Algorithms For Solving Variable-Order Fractional Percolation Equations, M. A. Abdelkawy

Applications and Applied Mathematics: An International Journal (AAM)

A high accurate spectral algorithm for one-dimensional variable-order fractional percolation equations (VO-FPEs) is considered.We propose a shifted Legendre Gauss-Lobatto collocation (SL-GLC) method in conjunction with shifted Chebyshev Gauss-Radau collocation (SC-GR-C) method to solve the proposed problem. Firstly, the solution and its space fractional derivatives are expanded as shifted Legendre polynomials series. Then, we determine the expansion coefficients by reducing the VO-FPEs and its conditions to a system of ordinary differential equations (SODEs) in time. The numerical approximation of SODEs is achieved by means of the SC-GR-C method. The under-study’s problem subjected to the Dirichlet or non-local boundary conditions is presented …

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Multilayer Security Of Rgb Image In Discrete Hartley Domain, Umar H. Mir, Deep Singh, D. C. Mishra, Parveiz N. Lone Dec 2020

Multilayer Security Of Rgb Image In Discrete Hartley Domain, Umar H. Mir, Deep Singh, D. C. Mishra, Parveiz N. Lone

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we present RGB image encryption and decryption using random matrix affine cipher (RMAC) associated with discrete Hartley transform (DHT) and random matrix shift cipher (RMSC). The parameters in RMAC and RMSC phases act as two series of secret keys whose arrangement is imperative in the proposed algorithm. The computer simulations with results and examples are given to analyze the efficiency of the proposed approach. Further, security analysis and comparison with the prior techniques successfully supports the robustness and validation of the proposed technique.

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Approximate Solutions For The Nonlinear Systems Of Algebraic Equations Using The Power Series Method, M. M. Khader, M. Adel Dec 2020

Approximate Solutions For The Nonlinear Systems Of Algebraic Equations Using The Power Series Method, M. M. Khader, M. Adel

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the approximate solutions for systems of nonlinear algebraic equations by the power series method (PSM) are presented. Illustrative examples have been presented to demonstrate the efficiency of the proposed method. In addition, the obtained results are compared with those obtained from the standard Adomian decomposition method. It turns out that the convergence of the proposed algorithm is rapid.

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On Higher-Order Duality In Nondifferentiable Minimax Fractional Programming, S. Al-Homidan, Vivek Singh, I. Ahmad Dec 2020

On Higher-Order Duality In Nondifferentiable Minimax Fractional Programming, S. Al-Homidan, Vivek Singh, I. Ahmad

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider a nondifferentiable minimax fractional programming problem with continuously differentiable functions and formulated two types of higher-order dual models for such optimization problem.Weak, strong and strict converse duality theorems are derived under higherorder generalized invexity.

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An Efficient Algorithm For Numerical Inversion Of System Of Generalized Abel Integral Equations, Sandeep Dixit Dec 2020

An Efficient Algorithm For Numerical Inversion Of System Of Generalized Abel Integral Equations, Sandeep Dixit

Applications and Applied Mathematics: An International Journal (AAM)

In this article a direct method is introduced, which is based on orthonormal Bernstein polynomials, to present an efficient and stable algorithm for numerical inversion of the system of singular integral equations of Abel type. The appropriateness of earlier numerical inversion methods was restricted to the one portion of singular integral equations of Abel type. The proposed method is absolutely accurate, and numerical illustrations are given to show the convergence and utilization of the suggested method and comparisons are made with some other existing numerical solution.

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Integrated Farm Model For Optimal Allocation Of Resources- A Linear Programming Approach, Mahak Bhatia, Anil Rana Dec 2020

Integrated Farm Model For Optimal Allocation Of Resources- A Linear Programming Approach, Mahak Bhatia, Anil Rana

Applications and Applied Mathematics: An International Journal (AAM)

The mathematical model for optimal allocation of farm resources, especially land and water are proposed to optimize the resources that contribute to increase farm revenues. A study is being carried out, to analyze the cropping practice adopted by growers, depending on availability and accessibility of resources. Different crop-combinations and cropping patterns are being analyzed in districts of Rajasthan. Rajasthan has arid topography with varying weather conditions. Thus, a diverse crop variety is being cultivated in a region. Being a state with inadequate water resources, the formulated model proposed different crop combinations alternatives. A crop-mix model is developed to reduce the …

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Analysis Of Map/Ph/1 Queueing Model With Breakdown, Instantaneous Feedback And Server Vacation, G. Ayyappan, K. Thilagavathy Dec 2020

Analysis Of Map/Ph/1 Queueing Model With Breakdown, Instantaneous Feedback And Server Vacation, G. Ayyappan, K. Thilagavathy

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we analyze a single server queueing model with feedback, a single vacation under Bernoulli schedule, breakdown and repair. The arriving customers follow the Markovian Arrival Process (MAP) and service follow the phase-type distribution. When the server returns from vacation, if there is no one present in the system, the server will wait until the customer’s arrival. When the service completion epoch if the customer is not satisfied then that customer will get the service immediately. Under the steady-state probability vector that the total number of customers are present in the system is probed by the Matrix-analytic method. …

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Mathematical Modeling For Studying The Sustainability Of Plants Subject To The Stress Of Two Distinct Herbivores, B. Chen-Charpentier, M. C.A. Leite, O. Gaoue, F. B. Agusto Jun 2020

Mathematical Modeling For Studying The Sustainability Of Plants Subject To The Stress Of Two Distinct Herbivores, B. Chen-Charpentier, M. C.A. Leite, O. Gaoue, F. B. Agusto

Applications and Applied Mathematics: An International Journal (AAM)

Viability of plants, especially endangered species, are usually affected by multiple stressors, including insects, herbivores, environmental factors and other plant species. We present new mathematical models, based on systems of ordinary differential equations, of two distinct herbivore species feeding (two stressors) on the same plant species. The new feature is the explicit functional form modeling the simultaneous feedback interactions (synergistic or additive or antagonistic) between the three species in the ecosystem. The goal is to investigate whether the coexistence of the plant and both herbivore species is possible (a sustainable system) and under which conditions sustainability is feasible. Our theoretical …

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Exploring The Convergence Properties Of A New Modified Newton-Raphson Root Method, Euaggelo E. Zotos, Wei Chen Jun 2020

Exploring The Convergence Properties Of A New Modified Newton-Raphson Root Method, Euaggelo E. Zotos, Wei Chen

Applications and Applied Mathematics: An International Journal (AAM)

We examine the convergence properties of a modified Newton-Raphson root method, by using a simple complex polynomial equation, as a test example. In particular, we numerically investigate how a parameter, entering the iterative scheme, affects the efficiency and the speed of the method. Color-coded polynomiographs are deployed for presenting the regions of convergence, as well as the fractality degree of the complex plane. We demonstrate that the behavior of the modified Newton-Raphson method is correlated with the numerical value of the parameter 1. Additionally, there are cases for which the method works flawlessly, while in some other cases we encounter …

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Basins Of Convergence In The Collinear Restricted Four-Body Problem With A Repulsive Manev Potential, Euaggelos E. Zotos, Md Sanam Suraj, Rajiv Aggarwal, Charanpreet Kaur Jun 2020

Basins Of Convergence In The Collinear Restricted Four-Body Problem With A Repulsive Manev Potential, Euaggelos E. Zotos, Md Sanam Suraj, Rajiv Aggarwal, Charanpreet Kaur

Applications and Applied Mathematics: An International Journal (AAM)

The Newton-Raphson basins of convergence, related to the equilibrium points, in the collinear restricted four-body problem with repulsive Manev potential are numerically investigated. We monitor the parametric evolution of the position as well as of the stability of the equilibrium points, as a function of the parameter e. The multivariate Newton-Raphson optimal method is used for revealing the basins of convergence, by classifying dense grids of initial conditions in several types of two-dimensional planes. We perform a systematic and thorough analysis in an attempt to understand how the parameter e affects the geometry as well as the basin entropy …

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Dynamic Optimal Control For Multi-Chemotherapy Treatment Of Dual Listeriosis Infection In Human And Animal Population, B. Echeng Bassey Jun 2020

Dynamic Optimal Control For Multi-Chemotherapy Treatment Of Dual Listeriosis Infection In Human And Animal Population, B. Echeng Bassey

Applications and Applied Mathematics: An International Journal (AAM)

Following the rising cases of high hospitalization versa-vise incessant fatality rates and the close affinity of listeriosis with HIV/AIDS infection, which often emanates from food-borne pathogens associated with listeria monocytogenes infection, this present paper seek and formulated as penultimate model, an 8-Dimensional classical mathematical Equations which directly accounted for the biological interplay of dual listeriosis virions with dual set of population (human and animals). The model was studied under multiple chemotherapies (trimethoprim-sulphamethoxazole with a combination of penicillin or ampicillin and/or gentamicin). Using ODE’s, the positivity and boundedness of system solutions was investigated with model presented as an optimal control problem. …

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Non-Uniform Haar Wavelet Method For Solving Singularly Perturbed Differential Difference Equations Of Neuronal Variability, Akmal Raza, Arshad Khan Apr 2020

Non-Uniform Haar Wavelet Method For Solving Singularly Perturbed Differential Difference Equations Of Neuronal Variability, Akmal Raza, Arshad Khan

Applications and Applied Mathematics: An International Journal (AAM)

A non-uniform Haar wavelet method is proposed on specially designed non-uniform grid for the numerical treatment of singularly perturbed differential-difference equations arising in neuronal variability.We convert the delay and shift terms using Taylor series up to second order and then the problem with delay and shift is converted into a new problem without the delay and shift terms. Then it is solved by using non-uniform Haar wavelet. Two test examples have been demonstrated to show the accuracy of the non-uniform Haar wavelet method. The performance of the present method yield more accurate results on increasing the resolution level and converges …

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An (S - 1; S) Inventory System With Negative Arrivals And Multiple Vacations, Kathiresan Jothivel, Anbazhagan Neelamegam Dec 2019

An (S - 1; S) Inventory System With Negative Arrivals And Multiple Vacations, Kathiresan Jothivel, Anbazhagan Neelamegam

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider a continuous review one-to-one ordering policy inventory system with multiple vacations and negative customers. The maximum storage capacity is S. The customers arrive according to a Poisson process with finite waiting hall. There are two types of customers: ordinary and negative. An ordinary customer, on arrival, joins the queue and the negative customer does not join the queue and takes away any one of the waiting customers. When the waiting hall is full, the arriving primary customer is considered to be lost. The service time and lead time are assumed to have independent exponential distribution. …

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Non-Standard Finite Difference Schemes For Investigating Stability Of A Mathematical Model Of Virus Therapy For Cancer, A. R. Yaghoubi, H. S. Najafi Dec 2019

Non-Standard Finite Difference Schemes For Investigating Stability Of A Mathematical Model Of Virus Therapy For Cancer, A. R. Yaghoubi, H. S. Najafi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a special case of finite difference method called non-standard finite difference (NSFD) method was studied to compute the numerical solutions of the nonlinear mathematical model of the interaction between tumor cells and oncolytic viruses. The global stability of the equilibrium points of the discrete model is investigated by using the Lyapunov stability theorem. Some conditions were gained for the local asymptotical stability of the equilibrium points of the system. Finally, numerical simulations are carried out to illustrate the main theoretical results. The discrete system is dynamically consistent with its continuous model, it preserves essential properties, such as …

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Solutions Of The Generalized Abel’S Integral Equation Using Laguerre Orthogonal Approximation, N. Singha, C. Nahak Dec 2019

Solutions Of The Generalized Abel’S Integral Equation Using Laguerre Orthogonal Approximation, N. Singha, C. Nahak

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a numerical approximation is drafted for solving the generalized Abel’s integral equation by practicing Laguerre orthogonal polynomials. The proposed approximation is framed for the first and second kinds of the generalized Abel’s integral equation. We have utilized the properties of fractional order operators to interpret Abel’s integral equation as a fractional integral equation. It offers a new approach by employing Laguerre polynomials to approximate the integrand of a fractional integral equation. Given examples demonstrate the simplicity and suitability of the method. The graphical representation of exact and approximate solutions helps in visualizing a solution at discrete points, …

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An Admm-Factorization Algorithm For Low Rank Matrix Completion, Rahman Taleghani, Maziar Salahi Dec 2019

An Admm-Factorization Algorithm For Low Rank Matrix Completion, Rahman Taleghani, Maziar Salahi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we propose an Alternating Direction Method of Multipliers (ADMM) based algorithm that is taking advantage of factorization for the fixed rank matrix completion problem. The convergence of the proposed algorithm to the KKT point is discussed. Finally, on several classes of test problems, its efficiency is compared with several efficient algorithms from the literature.

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Analysis Of Batch Arrival Single And Bulk Service Queue With Multiple Vacation Closedown And Repair, T. Deepa, A. Azhagappan Dec 2019

Analysis Of Batch Arrival Single And Bulk Service Queue With Multiple Vacation Closedown And Repair, T. Deepa, A. Azhagappan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we analyze batch arrival single and bulk service queueing model with multiple vacation, closedown and repair. The single server provides single service if the queue size is ‘< a’ and bulk service if the queue size is ‘ ≥ a’. After completing the service (single or bulk), the server may breakdown with probability ξ and then it will be sent for repair. When the system becomes empty or the server is ready to serve after the repair but no one is waiting, the server resumes closedown and then goes for a multiple vacation of random length. Using supplementary variable technique, the steady-state probability generating function (PGF) of …

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A Certain Class Of Statistical Deferred Weighted A-Summability Based On (P; Q)-Integers And Associated Approximation Theorems, L. N. Mishra, M. Patro, S. K. Paikray, B. B. Jena Dec 2019

A Certain Class Of Statistical Deferred Weighted A-Summability Based On (P; Q)-Integers And Associated Approximation Theorems, L. N. Mishra, M. Patro, S. K. Paikray, B. B. Jena

Applications and Applied Mathematics: An International Journal (AAM)

Statistical summability has recently enhanced researchers’ substantial awareness since it is more broad than the traditional (ordinary) convergence. The basic concept of statistical weighted A- summability was introduced by Mohiuddine (2016). In this investigation, we introduce the (presumably new) concept of statistical deferred weighted A-summability and deferred weighted A- statistical convergence with respect to the difference sequence of order r involving (p; q)-integers and establish an inclusion relation between them. Furthermore, based upon the proposed methods, we intend to approximate the rate of convergence and to demonstrate a Korovkin type approximation theorem for functions of two variables defined on a …

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An Efficient Computational Method For Solving A System Of Fdes Via Fractional Finite Difference Method, M. M. Khader, Sunil Kumar Dec 2019

An Efficient Computational Method For Solving A System Of Fdes Via Fractional Finite Difference Method, M. M. Khader, Sunil Kumar

Applications and Applied Mathematics: An International Journal (AAM)

This paper aims to provide a numerical method for solving systems of fractional (Caputo sense) differential equations (FDEs). This method is based on the fractional finite difference method (FDM), where we implemented the Grünwald-Letnikov’s approach. This method is computationally very efficient and gives very accurate solutions. In this study, the stability of the obtained numerical scheme is given. The numerical results show that the proposed approach is easy to be implemented and are accurate when applied to system of FDEs. The method introduces promising tool for solving many systems of FDEs. Two examples are given to demonstrate the applicability and …

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Numerical Solution Of Fractional Partial Differential Equations With Normalized Bernstein Wavelet Method, Mahsa Entezari, Saeid Abbasbandy, Esmail Babolian Dec 2019

Numerical Solution Of Fractional Partial Differential Equations With Normalized Bernstein Wavelet Method, Mahsa Entezari, Saeid Abbasbandy, Esmail Babolian

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, normalized Bernstein wavelets are presented. Next, the fractional order integration and Bernstein wavelets operational matrices of integration are derived and finally are used for solving fractional partial differential equations. The operational matrices merged with the collocation method are used in order to convert fractional problems to a number of algebraic equations. In the suggested method the boundary conditions are automatically taken into consideration. An assessment of the error of function approximation based on the normalized Bernstein wavelet is also presented. Some numerical instances are given to manifest the versatility and applicability of the suggested method. Founded numerical …

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