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Applications and Applied Mathematics: An International Journal (AAM)

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Articles 121 - 150 of 236

Full-Text Articles in Numerical Analysis and Computation

Numerical Solution Of Fractional Elliptic Pde's By The Collocation Method, Fuat Usta Jun 2017

Numerical Solution Of Fractional Elliptic Pde's By The Collocation Method, Fuat Usta

Applications and Applied Mathematics: An International Journal (AAM)

In this presentation a numerical solution for the solution of fractional order of elliptic partial differential equation in R2 is proposed. In this method we use the Radial basis functions (RBFs) method to benefit the desired properties of mesh free techniques such as no need to generate any mesh and easily applied to multi dimensions. In the numerical solution approach the RBF collocation method is used to discrete fractional derivative terms with the Gaussian basis function. Two dimensional numerical examples are presented and discussed, which conform well with the corresponding exact solutions.

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A Simple Linear Time Algorithm For Computing A 1-Median On Cactus Graphs, Kien T. Nguyen, Pham V. Chien, Ly H. Hai, Huynh D. Quoc Jun 2017

A Simple Linear Time Algorithm For Computing A 1-Median On Cactus Graphs, Kien T. Nguyen, Pham V. Chien, Ly H. Hai, Huynh D. Quoc

Applications and Applied Mathematics: An International Journal (AAM)

We address the problem of finding a 1-median on a cactus graph. The problem has already been solved in linear time by the algorithms of Burkard and Krarup (1998), and Lan and Wang (2000). These algorithms are complicated and need efforts. Hence, we develop in this paper a simpler algorithm. First, we construct a condition for a cycle that contains a 1-median or for a vertex that is indeed a 1-median of the cactus. Based on this condition, we localize the search for deriving a 1-median on the underlying cactus. Complexity analysis shows that the approach runs in linear time.

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Numerical Solution Of Fractional Integro-Differential Equations With Nonlocal Conditions, M. Jani, D. Bhatta, S. Javadi Jun 2017

Numerical Solution Of Fractional Integro-Differential Equations With Nonlocal Conditions, M. Jani, D. Bhatta, S. Javadi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present a numerical method for solving fractional integro-differential equations with nonlocal boundary conditions using Bernstein polynomials. Some theoretical considerations regarding fractional order derivatives of Bernstein polynomials are discussed. The error analysis is carried out and supported with some numerical examples. It is shown that the method is simple and accurate for the given problem.

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Numerical Study Of Soliton Solutions Of Kdv, Boussinesq, And Kaup-Kuperschmidt Equations Based On Jacobi Polynomials, Khadijeh Sadri, Hamideh Ebrahimi Jun 2017

Numerical Study Of Soliton Solutions Of Kdv, Boussinesq, And Kaup-Kuperschmidt Equations Based On Jacobi Polynomials, Khadijeh Sadri, Hamideh Ebrahimi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a numerical method is developed to approximate the soliton solutions of some nonlinear wave equations in terms of the Jacobi polynomials. Wave are very important phenomena in dispersion, dissipation, diffusion, reaction, and convection. Using the wave variable converts these nonlinear equations to the nonlinear ODE equations. Then, the operational Collocation method based on Jacobi polynomials as bases is applied to approximate the solution of ODE equation resulted. In addition, the intervals of the solution will be extended using an rational exponential approximation (REA). The KdV, Boussinesq, and Kaup–Kuperschmidt equations are studied as the test examples. Finally, numerical …

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Finite Difference Schemes For Variable Order Time-Fractional First Initial Boundary Value Problems, Gunvant A. Birajdar, M. M. Rashidi Jun 2017

Finite Difference Schemes For Variable Order Time-Fractional First Initial Boundary Value Problems, Gunvant A. Birajdar, M. M. Rashidi

Applications and Applied Mathematics: An International Journal (AAM)

The aim of the study is to obtain the numerical solution of first initial boundary value problem (IBVP) for semi-linear variable order fractional diffusion equation by using different finite difference schemes. We developed the three finite difference schemes namely explicit difference scheme, implicit difference scheme and Crank-Nicolson difference scheme, respectively for variable order type semi-linear diffusion equation. For this scheme the stability as well as convergence are studied via Fourier method. At the end, solution of some numerical examples are discussed and represented graphically using Matlab.

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A Numerical Scheme For Generalized Fractional Optimal Control Problems, N. Singha, C. Nahak Dec 2016

A Numerical Scheme For Generalized Fractional Optimal Control Problems, N. Singha, C. Nahak

Applications and Applied Mathematics: An International Journal (AAM)

This paper introduces a generalization of the Fractional Optimal Control Problem (GFOCP). Proposed generalizations differ in terms of explaining the constraint involved in the dynamical system of the control problem. We assume the constraint as an arbitrary function of fractional derivatives and fractional integrals. By this assumption the restriction on constraint, to be of some prescribed function of fractional operators, is removed. Deduction of necessary optimality conditions followed by particular cases and examples has been provided. Additionally, we construct a solution scheme for the suggested class of (GFOCP)’s. The formulation of this scheme is done by implementing the Adomian decomposition …

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On The Slow Growth And Approximation Of Entire Function Solutions Of Second-Order Elliptic Partial Differential Equations On Caratheodory Domains, Devendra Kumar Dec 2016

On The Slow Growth And Approximation Of Entire Function Solutions Of Second-Order Elliptic Partial Differential Equations On Caratheodory Domains, Devendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we consider the regular, real-valued solutions of the second-order elliptic partial differential equation. The characterization of generalized growth parameters for entire function solutions for slow growth in terms of approximation errors on more generalized domains, i.e., Caratheodory domains, has been obtained. Moreover, we studied some inequalities concerning the growth parameters of entire function solutions of above equation for slow growth which have not been studied so far.

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Implementation Of The Matrix Differential Transform Method For Obtaining An Approximate Solution Of Some Nonlinear Matrix Evolution Equations, M. M. Khader, A. Borhanifar Dec 2016

Implementation Of The Matrix Differential Transform Method For Obtaining An Approximate Solution Of Some Nonlinear Matrix Evolution Equations, M. M. Khader, A. Borhanifar

Applications and Applied Mathematics: An International Journal (AAM)

This article introduces the matrix differential transform method (MDTM) to apply to matrix partial differential equations (MPDEs) and employs it for solving matrix Fisher equations, matrix Burgers equations and matrix KdV equations. We show how the MDTM applies to the linear part and nonlinear part of any MPDE and give various examples of MPDEs to illustrate the efficiency of the method. The results obtained are in excellent agreement with the exact solution and show that the proposed method is powerful, accurate, and easy.

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Non Markovian Queue With Two Types Service Optional Re-Service And General Vacation Distribution, K. Sathiya, G. Ayyappan Dec 2016

Non Markovian Queue With Two Types Service Optional Re-Service And General Vacation Distribution, K. Sathiya, G. Ayyappan

Applications and Applied Mathematics: An International Journal (AAM)

We consider a single server batch arrival queueing system, where the server provides two types of heterogeneous service. A customer has the option of choosing either type 1 service with probability p1 or type 2 service with probability p2 with the service times follow general distribution. After the completion of either type 1 or type 2 service a customer has the option to repeat or not to repeat the type 1 or type 2 service. As soon as the customer service is completed, the server will take a vacation with probability θ or may continue staying in the system with …

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Some Results On F-Simultaneous Chebyshev Approximation, Sh. Al-Sharif, Kh. Qaraman Dec 2016

Some Results On F-Simultaneous Chebyshev Approximation, Sh. Al-Sharif, Kh. Qaraman

Applications and Applied Mathematics: An International Journal (AAM)

Let X be Hausdorff topological vector space and f be a real valued continuous function on X: In this paper we introduce and study the concept of f-simultaneous approximation of a nonempty subset K of X as a generalization to the problem of simultaneous approximation. Further we present some results regarding f-simultaneous approximation in the quotient space.

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Markov Chain Profit Modelling And Evaluation Between Two Dissimilar Systems Under Two Types Of Failures, Saminu I. Bala, Ibrahim Yusuf Dec 2016

Markov Chain Profit Modelling And Evaluation Between Two Dissimilar Systems Under Two Types Of Failures, Saminu I. Bala, Ibrahim Yusuf

Applications and Applied Mathematics: An International Journal (AAM)

No abstract provided.

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A 10-Point Approximating Subdivision Scheme Based On Least Squares Technique, Ghulam Mustafa, Muhammad T. Iqbal Dec 2016

A 10-Point Approximating Subdivision Scheme Based On Least Squares Technique, Ghulam Mustafa, Muhammad T. Iqbal

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a 10-point approximating subdivision scheme is presented. Least squares technique for fitting the polynomial of degree 9 to data is used to develop this scheme. The proposed strategy can be used to generate a family of schemes. The important characteristics of the scheme are also discussed. Graphical efficiency of the scheme is shown by applying it on different types of data.

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Non-Newtonian Prandtl Fluid Over Stretching Permeable Surface, N. R. Jain, M. G. Timol Jun 2016

Non-Newtonian Prandtl Fluid Over Stretching Permeable Surface, N. R. Jain, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

An analysis is made of the velocity and temperature distribution in the flow of a viscous incompressible fluid caused by the stretching permeable surface which issues in the Prandtl fluid. Parandtl fluid is a pseudoplastic visco-inelastic non-Newtonian fluid. The governing partial differential equations are reduced to ordinary differential equations using deductive group transformation and similarity solution is derived. Numerical solutions to the reduced non-linear similarity equations are then obtained by adopting shooting method using the Nachtsheim-Swigert iteration technique. The results of the numerical solution are then presented graphically in the form of velocity and temperature profiles. The corresponding skin friction …

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Color Image Encryption And Decryption Using Hill Cipher Associated With Arnold Transform, Rakesh Ranjan, R. K. Sharma, M. Hanmandlu Jun 2016

Color Image Encryption And Decryption Using Hill Cipher Associated With Arnold Transform, Rakesh Ranjan, R. K. Sharma, M. Hanmandlu

Applications and Applied Mathematics: An International Journal (AAM)

Image security over open network transmission is a big concern nowadays. This paper proposes another methodology for color image encoding and decoding using two stage Hill Cipher method which is connected with Arnold Transformation. The forgoing created a strategy for encryption and decryption of color image information and touched on just the premise of keys. In this plan, keys and the agreement of Hill Cipher (HC) are basic. Moreover, keys multiplication (pre or post) over an RGB image information framework is inevitable to know to effectively decrypt the first image information. We have given a machine simulation with a standard …

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Dynamic Network Flows With Uncertain Costs Belonging To Interval, Gholam H. Shirdel, Hassan Rezapour Jun 2016

Dynamic Network Flows With Uncertain Costs Belonging To Interval, Gholam H. Shirdel, Hassan Rezapour

Applications and Applied Mathematics: An International Journal (AAM)

This paper considers minimum cost flow problem in dynamic networks with uncertain costs. First, we present a short introduction of dynamic minimum cost flow. Then, we survey discrete and continuous dynamic minimum cost flow problems, their properties and relationships between them. After that, the minimum cost flow problem in discrete dynamic network with uncertainty in the cost vector is considered such that the arc cost can be changed within an interval. Finally, we propose an algorithm to find the optimal solution of the proposed model.

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Some Results On F-Simultaneous Chebyshev Approximation, Sh. Al-Sharif, Kh. Qaraman Jun 2016

Some Results On F-Simultaneous Chebyshev Approximation, Sh. Al-Sharif, Kh. Qaraman

Applications and Applied Mathematics: An International Journal (AAM)

Let X be a Hausdorff topological vector space and f be a real valued continuous function on X: In this paper we introduce and study the concept of f􀀀simultaneous approximation of a nonempty subset K of X as a generalization to the problem of simultaneous approximation. Further we present some results regarding f􀀀simultaneous approximation in the quotient space.

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Construction Of Energy Preserving Qmf, Jian-Ao Lian, Yonghui Wang Jun 2016

Construction Of Energy Preserving Qmf, Jian-Ao Lian, Yonghui Wang

Applications and Applied Mathematics: An International Journal (AAM)

Recently, a family of perfect reconstruction (PR) quadrature mirror filterbanks (QMF) with finite impulse response filters (FIR) from systems of biorthogonal refinable functions and wavelets were introduced and also applied to image processing. However, a detailed procedure was absent. The main objective of this paper is to present extensive examples that will provide a thorough process of construction of the new family of PR QMF with FIR filterbanks. These new filters are linearphase due to the symmetry property of their corresponding biorthogonal refinable functions and wavelets. In addition, these filters have odd lengths so that the symmetric extension can be …

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Priority Queueing System With A Single Server Serving Two Queues M[X1],M[X2]/G1,G2/1 With Balking And Optional Server Vacation, G. Ayyappan, P. Thamizhselvi Jun 2016

Priority Queueing System With A Single Server Serving Two Queues M[X1],M[X2]/G1,G2/1 With Balking And Optional Server Vacation, G. Ayyappan, P. Thamizhselvi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we study a vacation queueing system with a single server simultaneously dealing with an M[x1] /G1/1 and an M[x2] /G2/1 queues. Two classes of units, priority and non-priority, arrive at the system in two independent compound Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority and non-priority units. We further assume that the server may take a vacation of random length just after serving the last customer in the priority unit present in the system. If the server …

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A Robust Uniform B-Spline Collocation Method For Solving The Generalized Phi-Four Equation, W. K. Zahra, W. A. Ouf, M. S. El-Azab Jun 2016

A Robust Uniform B-Spline Collocation Method For Solving The Generalized Phi-Four Equation, W. K. Zahra, W. A. Ouf, M. S. El-Azab

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we develop a numerical solution based on cubic B-spline collocation method. By applying Von-Neumann stability analysis, the proposed technique is shown to be unconditionally stable. The accuracy of the presented method is demonstrated by a test problem. The numerical results are found to be in good agreement with the exact solution.

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Cobb-Douglas Based Firm Production Model Under Fuzzy Environment And Its Solution Using Geometric Programming, Palash Mandal, Arindam Garai, Tapan K. Roy Jun 2016

Cobb-Douglas Based Firm Production Model Under Fuzzy Environment And Its Solution Using Geometric Programming, Palash Mandal, Arindam Garai, Tapan K. Roy

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider Cobb-Douglas production function based model in a firm under fuzzy environment, and its solution technique by making use of geometric programming. A firm may use many finite inputs such as labour, capital, coal, iron etc. to produce one single output. It is well known that the primary intention of using production function is to determine maximum output for any given combination of inputs. Also, the firm may gain competitive advantages if it can buy and sell in any quantities at exogenously given prices, independent of initial production decisions. On the other hand, in reality, constraints …

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Viscous Dissipation And Heat Absorption Effect On Natural Convection Flow With Uniform Surface Temperature Along A Vertical Wavy Surface, Sujon Nath, Nazma Parveen May 2016

Viscous Dissipation And Heat Absorption Effect On Natural Convection Flow With Uniform Surface Temperature Along A Vertical Wavy Surface, Sujon Nath, Nazma Parveen

Applications and Applied Mathematics: An International Journal (AAM)

The effect of viscous dissipation and heat absorption on a steady two-dimensional natural convection laminar flow of viscous incompressible fluid with uniform surface temperature along a vertical wavy surface has been investigated. Using the appropriate variables; the basic equations are transformed to convenient form and then solved numerically employing very efficient method, namely Keller-Box method (KBM). Numerical results are presented by the shearing stress in terms of the local skin-friction coefficient; the rate of heat transfer in terms of local Nusselt number, streamline and isotherms, respectively for a wide range of the viscous dissipation parameter N and heat absorption parameter …

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Prandtl Number Effect On Assisted Convective Heat Transfer Through A Solar Collector, Rehen Nasrin, Salma Parvin, M. A. Alim May 2016

Prandtl Number Effect On Assisted Convective Heat Transfer Through A Solar Collector, Rehen Nasrin, Salma Parvin, M. A. Alim

Applications and Applied Mathematics: An International Journal (AAM)

Numerical study of the influence of Prandtl number on forced convective heat transfer through a riser pipe of a flat plate solar collector is done. The working fluid is Al2O3/water nanofluid. By Finite Element Method the governing partial differential equations are solved. The effect of the Prandtl number on the temperature and velocity field has been depicted. Comprehensive average Nusselt number, average bulk temperature, mean velocity, mid-height temperature inside the pipe, mean output temperature and collector efficiency are presented for the governing parameter mentioned above. Nu increases by 16% with the variation of Pr from 4.6 to 6.6 using nanofluid. …

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Stability Condition Of A Retrial Queueing System With Abandoned And Feedback Customers, Amina A. Bouchentouf, Abbes Rabhi, Lahcene Yahiaoui Dec 2015

Stability Condition Of A Retrial Queueing System With Abandoned And Feedback Customers, Amina A. Bouchentouf, Abbes Rabhi, Lahcene Yahiaoui

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with the stability of a retrial queueing system with two orbits, abandoned and feedback customers. Two independent Poisson streams of customers arrive to the system, and flow into a single-server service system. An arriving one of type i; i = 1; 2, is handled by the server if it is free; otherwise, it is blocked and routed to a separate type-i retrial (orbit) queue that attempts to re-dispatch its jobs at its specific Poisson rate. The customer in the orbit either attempts service again after a random time or gives up receiving service and leaves the system …

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Approximate Solutions For The Flow And Heat Transfer Due To A Stretching Sheet Embedded In A Porous Medium With Variable Thickness, Variable Thermal Conductivity And Thermal Radiation Using Laguerre Collocation Method, M. M. Khader, Ahmed M. Megahed Dec 2015

Approximate Solutions For The Flow And Heat Transfer Due To A Stretching Sheet Embedded In A Porous Medium With Variable Thickness, Variable Thermal Conductivity And Thermal Radiation Using Laguerre Collocation Method, M. M. Khader, Ahmed M. Megahed

Applications and Applied Mathematics: An International Journal (AAM)

In this article, a numerical approach is given for studying the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with a power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by a non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing PDEs are transformed into a system of coupled non-linear ODEs which are using appropriate boundary conditions for various physical parameters. The proposed method is based on replacement of the unknown function by truncated series …

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Numerical Solution Of Linear Fredholm Integro-Differential Equations By Non-Standard Finite Difference Method, Pramod K. Pandey Dec 2015

Numerical Solution Of Linear Fredholm Integro-Differential Equations By Non-Standard Finite Difference Method, Pramod K. Pandey

Applications and Applied Mathematics: An International Journal (AAM)

In this article we consider a non-standard finite difference method for numerical solution of linear Fredholm integro-differential equations. The non-standard finite difference method and the repeated / composite trapezoidal quadrature method are used to transform the Fredholm integro-differential equation into a system of non-linear algebraic equations. The numerical experiments on some linear model problems show the simplicity and efficiency of the proposed method. It is observed from the numerical experiments that our method is convergent and second order accurate.

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Group Decision Making Using Comparative Linguistic Expression Based On Hesitant Intuitionistic Fuzzy Sets, Ismat Beg, Tabasam Rashid Dec 2015

Group Decision Making Using Comparative Linguistic Expression Based On Hesitant Intuitionistic Fuzzy Sets, Ismat Beg, Tabasam Rashid

Applications and Applied Mathematics: An International Journal (AAM)

We introduce a method for aggregation of experts’ opinions given in the form of comparative linguistic expression. An algorithmic form of technique for order preference is proposed for group decision making. A simple example is given by using this method for the selection of the best alternative as well as ranking the alternatives from the best to the worst.

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Differential Transform Method For Solving The Two-Dimensional Fredholm Integral Equations, F. Ziyaee, A. Tari Dec 2015

Differential Transform Method For Solving The Two-Dimensional Fredholm Integral Equations, F. Ziyaee, A. Tari

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we develop the Differential Transform (DT) method in a new scheme to solve the two-dimensional Fredholm integral equations (2D-FIEs) of the second kind. The differential transform method is a procedure to obtain the coefficients of the Taylor expansion of the solution of differential and integral equations. So, one can obtain the Taylor expansion of the solution of arbitrary order and hence the solution of the given equation can be obtained with required accuracy. Here, we first give some basic definitions and properties about DT from references, and then we prove some theorems to extend the DT method …

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Use Of Cubic B-Spline In Approximating Solutions Of Boundary Value Problems, Maria Munguia, Dambaru Bhatta Dec 2015

Use Of Cubic B-Spline In Approximating Solutions Of Boundary Value Problems, Maria Munguia, Dambaru Bhatta

Applications and Applied Mathematics: An International Journal (AAM)

Here we investigate the use of cubic B-spline functions in solving boundary value problems. First, we derive the linear, quadratic, and cubic B-spline functions. Then we use the cubic B-spline functions to solve second order linear boundary value problems. We consider constant coefficient and variable coefficient cases with non-homogeneous boundary conditions for ordinary differential equations. We also use this numerical method for the space variable to obtain solutions for second order linear partial differential equations. Numerical results for various cases are presented and compared with exact solutions.

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Laminar Boundary Layer Flow Of Sisko Fluid, Manisha Patel, Jayshri Patel, M. G. Timol Dec 2015

Laminar Boundary Layer Flow Of Sisko Fluid, Manisha Patel, Jayshri Patel, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

The problem of steady two dimensional laminar boundary layer flow of non-Newtonian fluid is analyzed in the present paper. Sisko fluid model, one of the various fluid models of non- Newtonian fluid, is considered for stress-strain relationship. Similarity and numerical solutions obtained for the defined flow problem.

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Algorithm For Solving Tri-Diagonal Finite Volume Discretized Linear Systems, J. S. V. R. Krishna Prasad, Parag V. Patil Dec 2015

Algorithm For Solving Tri-Diagonal Finite Volume Discretized Linear Systems, J. S. V. R. Krishna Prasad, Parag V. Patil

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we present efficient computational algorithms for solving finite volume discretized tri-diagonal linear systems. The implementation of the algorithm for steady state finite volume structured grids linear system using MS Excel is presented. An example is given in order to illustrate the algorithms.

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