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Articles 1 - 30 of 36
Full-Text Articles in Physical Sciences and Mathematics
Analytical Solutions For The Black-Scholes Equation, Jalil Manafian, Mahnaz Paknezhad
Analytical Solutions For The Black-Scholes Equation, Jalil Manafian, Mahnaz Paknezhad
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the Black-Sholes equation (BS) has been applied successfully with the Cauchy-Euler method and the method of separation of variables and new analytical solutions have been found. The linear partial differential equation (PDE) transformed to linear ordinary differential equation (ODE) as well. We acquired three types of solutions including hyperbolic, trigonometric and rational solutions. Descriptions of these methods are given and the obtained results reveal that three methods are tools for exploring partial differential models.
A New Hybrid Method For Solving Nonlinear Fractional Differential Equations, R. Delpasand, M. M. Hosseini, F. M. Maalek Ghaini
A New Hybrid Method For Solving Nonlinear Fractional Differential Equations, R. Delpasand, M. M. Hosseini, F. M. Maalek Ghaini
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, numerical solution of initial and boundary value problems for nonlinear fractional differential equations is considered by pseudospectral method. In order to avoid solving systems of nonlinear equations resulting from the method, the residual function of the problem is constructed, as well as a suggested unconstrained optimization model solved by PSOGSA algorithm. Furthermore, the research inspects and discusses the spectral accuracy of Chebyshev polynomials in the approximation theory. The following scheme is tested for a number of prominent examples, and the obtained results demonstrate the accuracy and efficiency of the proposed method.
Fractional Order Thermoelastic Deflection In A Thin Circular Plate, J. J. Tripathi, S. D. Warbhe, K. C. Deshmukh, J. Verma
Fractional Order Thermoelastic Deflection In A Thin Circular Plate, J. J. Tripathi, S. D. Warbhe, K. C. Deshmukh, J. Verma
Applications and Applied Mathematics: An International Journal (AAM)
In this work, a quasi-static uncoupled theory of thermoelasticity based on time fractional heat conduction equation is used to model a thin circular plate, whose lower surface is maintained at zero temperature whereas the upper surface is insulated. The edge of the circular plate is fixed and clamped. Integral transform technique is used to derive the analytical solutions in the physi-cal domain. The numerical results for temperature distributions and thermal deflection are com-puted and represented graphically for Copper material.
Numerical Experiments For Finding Roots Of The Polynomials In Chebyshev Basis, M. S. Solary
Numerical Experiments For Finding Roots Of The Polynomials In Chebyshev Basis, M. S. Solary
Applications and Applied Mathematics: An International Journal (AAM)
Root finding for a function or a polynomial that is smooth on the interval [a; b], but otherwise arbitrary, is done by the following procedure. First, approximate it by a Chebyshev polynomial series. Second, find the zeros of the truncated Chebyshev series. Finding roots of the Chebyshev polynomial is done by eigenvalues of a nXn matrix such as companion or comrade matrices. There are some methods for finding eigenvalues of these matrices such as companion matrix and chasing procedures.We derive another algorithm by second kind of Chebyshev polynomials.We computed the numerical results of these methods for some special and ill-conditioned …
Effective Modified Hybrid Conjugate Gradient Method For Large-Scale Symmetric Nonlinear Equations, Jamilu Sabi'u, Mohammed Y. Waziri
Effective Modified Hybrid Conjugate Gradient Method For Large-Scale Symmetric Nonlinear Equations, Jamilu Sabi'u, Mohammed Y. Waziri
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we proposed hybrid conjugate gradient method using the convex combination of FR and PRP conjugate gradient methods for solving Large-scale symmetric nonlinear equations via Andrei approach with nonmonotone line search. Logical formula for obtaining the convex parameter using Newton and our proposed directions was also proposed. Under appropriate conditions global convergence was established. Reported numerical results show that the proposed method is very promising.
The Fmx/Fm/1 Queue With Multiple Working Vacation, G. Kannadasan, N. Sathiyamoorthi
The Fmx/Fm/1 Queue With Multiple Working Vacation, G. Kannadasan, N. Sathiyamoorthi
Applications and Applied Mathematics: An International Journal (AAM)
This study investigates the batch arrival FMX/FM/1 queue with multiple working vacation. For this fuzzy queuing model, this research obtains some performance measure of interest such as mean system length, mean system sojourn time, mean busy period for the server and working vacation period. Finally, numerical results are presented to show the effects of system parameters.
Thermoelastic Analysis Of A Nonhomogeneous Hollow Cylinder With Internal Heat Generation, V. R. Manthena, N. K. Lamba, G. D. Kedar
Thermoelastic Analysis Of A Nonhomogeneous Hollow Cylinder With Internal Heat Generation, V. R. Manthena, N. K. Lamba, G. D. Kedar
Applications and Applied Mathematics: An International Journal (AAM)
In the present paper, we have determined the heat conduction and thermal stresses of a hollow cylinder with inhomogeneous material properties and internal heat generation. All the material properties except Poisson’s ratio and density are assumed to be given by a simple power law in axial direction. We have obtained the solution of the two dimensional heat conduction equation in the transient state in terms of Bessel’s and trigonometric functions. The influence of inhomogeneity on the thermal and mechanical behavior is examined. Numerical computations are carried out for both homogeneous and nonhomogeneous cylinders and are represented graphically.
Certain Integrals Associated With The Generalized Bessel-Maitland Function, D. L. Suthar, Hafte Amsalu
Certain Integrals Associated With The Generalized Bessel-Maitland Function, D. L. Suthar, Hafte Amsalu
Applications and Applied Mathematics: An International Journal (AAM)
The aim of this paper is to establish two general finite integral formulas involving the generalized Bessel-Maitland functions Jμ,γν,q (z). The result given in terms of generalized (Wright’s) hypergeometric functions pΨq and generalized hypergeometric functions pFq . These results are obtained with the help of finite integral due to Lavoie and Trottier. Some interesting special cases involving Bessel-Maitland function, Struve’s functions, Bessel functions, generalized Bessel functions, Wright function, generalized Mittag-Leffler functions are deduced.
Applications Of Planar Newtonian Four-Body Problem To The Central Configurations, M. R. Hassan, M. S. Ullah, Md. Aminul Hassan, Umakant Prasad
Applications Of Planar Newtonian Four-Body Problem To The Central Configurations, M. R. Hassan, M. S. Ullah, Md. Aminul Hassan, Umakant Prasad
Applications and Applied Mathematics: An International Journal (AAM)
The present study deals with the applications of the planar Newtonian four-body problem to
the different central configurations. The basic concept of central configuration is that the
vector force must be in the direction of the position vector so that the origin may be taken at
the centre of mass of the four bodies and the force towards the position vector multiplied by
corresponding inverse mass is directly proportional to the position vector relative to the
centre of mass. For applying the Newtonian four body problem to the central configuration,
the equations of motion of four bodies have been established …
Evaluation Of Some Reliability Characteristics Of A Single Unit System Requiring Two Types Of Supporting Device For Operations, Ibrahim Yusuf, Nura J. Fagge
Evaluation Of Some Reliability Characteristics Of A Single Unit System Requiring Two Types Of Supporting Device For Operations, Ibrahim Yusuf, Nura J. Fagge
Applications and Applied Mathematics: An International Journal (AAM)
This study presents the reliability assessment of a single unit connected to two types of external supporting devices for its operation. Each type of external supporting device has two copies I and II on standby. First order differential difference equations method is used to obtain the explicit expression for the steady state availability, busy period due to failure of type I and II supporting devices of repairmen, steady-state availability and profit function. Based on assumed numerical values given to system parameters, graphical illustrations are given to highlight important results. Comparisons are performed to highlight the impact of unit failure and …
On The Qualitative Behaviors Of A Functional Differential Equation Of Second Order, Cemil Tunç
On The Qualitative Behaviors Of A Functional Differential Equation Of Second Order, Cemil Tunç
Applications and Applied Mathematics: An International Journal (AAM)
The aim of this paper is first to investigate the stability of the zero solution to a new Liénard type equation with multiple variable delays by two different methods. The methods to be used in the proofs involve the Lyapunov-Krasovskiĭ functional approach and the fixed point technique under an exponentially weighted metric, respectively. We make a comparison between the applications of these methods with the established conditions on the same stability problems. Then, we obtain three new results for uniformly stability and boundedness/ uniformly boundedness of the solutions to the considered equation by the Lyapunov-Krasovskiĭ functional approach. An example is …
On The Lp-Spaces Techniques In The Existence And Uniqueness Of The Fuzzy Fractional Korteweg-De Vries Equation’S Solution, F. Farahrooz, A. Ebadian, S. Najafzadeh
On The Lp-Spaces Techniques In The Existence And Uniqueness Of The Fuzzy Fractional Korteweg-De Vries Equation’S Solution, F. Farahrooz, A. Ebadian, S. Najafzadeh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, is proposed the existence and uniqueness of the solution of all fuzzy fractional differential equations, which are equivalent to the fuzzy integral equation. The techniques on LP-spaces are used, defining the LpF F ([0; 1]) for 1≤P≤∞, its properties, and using the functional analysis methods. Also the convergence of the method of successive approximations used to approximate the solution of fuzzy integral equation be proved and an iterative procedure to solve such equations is presented.
Rate Of Convergence For Generalized Szász–Mirakyan Operators In Exponential Weighted Space, Sevilay K. Serenbay, Özge Dalmano˘Glu
Rate Of Convergence For Generalized Szász–Mirakyan Operators In Exponential Weighted Space, Sevilay K. Serenbay, Özge Dalmano˘Glu
Applications and Applied Mathematics: An International Journal (AAM)
In the present paper, generalized Szász–Mirakyan operators in exponential weighted space of functions of one variable are introduced. Using a method given by Rempulska and Walczak, some theorems on the degree of approximation are investigated. Furthermore, a numerical example with an illustrative graphic is given to show comparison for the error estimates of the operators.
Interactions Of Thermoelastic Beam In Modified Couple Stress Theory, Rajneesh Kumar, Shaloo Devi
Interactions Of Thermoelastic Beam In Modified Couple Stress Theory, Rajneesh Kumar, Shaloo Devi
Applications and Applied Mathematics: An International Journal (AAM)
This paper is concerned with the study of thermoelastic beam in modified couple stress theory. The governing equations of motion for modified couple stress theory and heat conduction equation for non-Fourier (non-classical process) are investigated to model the vibrations in a homogeneous isotropic thin beam in a closed form by employing the Euler Bernoulli beam theory. The generalized theories of thermoelasticity with one and two relaxation times are used to model the problem. Both ends of the beam are simply supported. The Laplace transform technique applied to solve the system of equations which are written in dimensionless form. A general …
Analytical Solution For Determination The Control Parameter In The Inverse Parabolic Equation Using Ham, M. M. Khader
Analytical Solution For Determination The Control Parameter In The Inverse Parabolic Equation Using Ham, M. M. Khader
Applications and Applied Mathematics: An International Journal (AAM)
In this article, the homotopy analysis method (HAM) for obtaining the analytical solution of the inverse parabolic problem and computing the unknown time-dependent parameter is introduced. The series solution is developed and the recurrence relations are given explicitly. Special attention is given to satisfy the convergence of the proposed method. A comparison of HAM with the variational iteration method is made. In the HAM, we use the auxiliary parameter ~ to control with a simple way in the convergence region of the solution series. Applying this method with several
A Novel Approach For Solving Volterra Integral Equations Involving Local Fractional Operator, Hassan K. Jassim
A Novel Approach For Solving Volterra Integral Equations Involving Local Fractional Operator, Hassan K. Jassim
Applications and Applied Mathematics: An International Journal (AAM)
The paper presents an approximation method called local fractional variational iteration method (LFVIM) for solving the linear and nonlinear Volterra integral equations of the second kind with local fractional derivative operators. Some illustrative examples are discussed to demonstrate the efficiency and the accuracy of the proposed method. Furthermore, this method does not require spatial discretization or restrictive assumptions and therefore reduces the numerical computation significantly. The results reveal that the local fractional variational iteration method is very effective and convenient to solve linear and nonlinear integral equations within local fractional derivative operators.
Thermal Stress Analysis In A Functionally Graded Hollow Elliptic-Cylinder Subjected To Uniform Temperature Distribution, V. R. Manthena, N. K. Lamba, G. D. Kedar
Thermal Stress Analysis In A Functionally Graded Hollow Elliptic-Cylinder Subjected To Uniform Temperature Distribution, V. R. Manthena, N. K. Lamba, G. D. Kedar
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, an analytical method of a thermoelastic problem for a medium with functionally graded material properties is developed in a theoretical manner for the elliptic-cylindrical coordinate system under the assumption that the material properties except for Poisson’s ratio and density are assumed to vary arbitrarily with the exponential law in the radial direction. An attempt has been made to reconsider the fundamental system of equations for functionally graded solids in a two-dimensional state under thermal and mechanical loads. The general solution of displacement formulation is obtained by the introduction of appropriate transformation and carried out the analysis by …
Numerical Solution Of Fractional Integro-Differential Equations With Nonlocal Conditions, M. Jani, D. Bhatta, S. Javadi
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.
Numerical Study Of Soliton Solutions Of Kdv, Boussinesq, And Kaup-Kuperschmidt Equations Based On Jacobi Polynomials, Khadijeh Sadri, Hamideh Ebrahimi
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 …
Effect Of Damping And Thermal Gradient On Vibrations Of Orthotropic Rectangular Plate Of Variable Thickness, U. S. Rana, Robin Robin
Effect Of Damping And Thermal Gradient On Vibrations Of Orthotropic Rectangular Plate Of Variable Thickness, U. S. Rana, Robin Robin
Applications and Applied Mathematics: An International Journal (AAM)
In this present paper, damped vibrations of an orthotropic rectangular plate resting on elastic foundation with thermal gradient is modeled, considering variable thickness of plate. Following Le`vy approach, the governed equation of motion is solved numerically using quintic spline technique with clamped and simply supported edges. The effect of damping parameter and thermal gradient together with taper constant, density parameter and elastic foundation parameter on the natural frequencies of vibration for the first three modes of vibration are depicted through Tables and Figures, and mode shapes have been computed for fixed value of plate parameter. It has been observed that …
Some Relations On Generalized Rice's Matrix Polynomials, Ayman Shehata
Some Relations On Generalized Rice's Matrix Polynomials, Ayman Shehata
Applications and Applied Mathematics: An International Journal (AAM)
The main aim of this paper is to obtain certain properties of generalized Rice’s matrix polynomials such as their matrix differential equation, generating matrix functions, an expansion for them. We have also deduced the various families of bilinear and bilateral generating matrix functions for them with the help of the generating matrix functions developed in the paper and some of their applications have also been presented here.
Application Of Taylor-Pade Technique For Obtaining Approximate Solution For System Of Linear Fredholm Integro-Dierential Equations, M. M. Khader
Applications and Applied Mathematics: An International Journal (AAM)
In this article, we introduce a modification of the Taylor matrix method using Pad´e approximation to obtain an accurate solution of linear system of Fredholm integro-differential equations (FIDEs). This modification is based on, first, taking truncated Taylor series of the functions and then substituting their matrix forms into the given equations. Thereby the equation reduces to a matrix equation, which corresponds to a system of linear algebraic equations with unknown Taylor coefficients. Finally, we use Pad´e approximation to obtain an accurate numerical solution of the proposed problem. To demonstrate the validity and the applicability of the proposed method, we present …
Inverse Problem For A Parabolic System, Reza Pourgholi, Amin Esfahani, Hassan D. Mazraeh
Inverse Problem For A Parabolic System, Reza Pourgholi, Amin Esfahani, Hassan D. Mazraeh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper a numerical approach combining the least squares method and a genetic algorithm is proposed for the determination of the source term in an inverse parabolic system (IPS). A numerical experiment confirm the utility of this algorithm as the results are in good agreement with the exact data. Results show that a reasonable estimation can be obtained by the genetic algorithm within a CPU with clock speed 2.7 GHz.
Damping In Microscale Modified Couple Stress Thermoelastic Circular Kirchhoff Plate Resonators, Rajneesh Kumar, Shaloo Devi, Veena Sharma
Damping In Microscale Modified Couple Stress Thermoelastic Circular Kirchhoff Plate Resonators, Rajneesh Kumar, Shaloo Devi, Veena Sharma
Applications and Applied Mathematics: An International Journal (AAM)
The vibrations of circular plate in modified couple stress thermoelastic medium using Kirchhoff- Love plate theory has been presented. The basic equations of motion and heat conduction equation for Lord Shulman (L-S, 1967) theory are written with the help of Kirchhoff-Love plate theory. The thermoelastic damping of micro beam resonators is studied by applying normal mode analysis method. The solutions for the free vibrations of plates under clamped, simply supported and free boundary conditions are obtained. The analytical expressions for thermoelastic damping of vibration and frequency shift are obtained for generalized couple stress thermoelastic and coupled thermoelastic plates. Numerical results …
Generalized Statistical Summability Of Double Sequences And Korovkin Type Approximation Theorem, M. Mursaleen
Generalized Statistical Summability Of Double Sequences And Korovkin Type Approximation Theorem, M. Mursaleen
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we introduce the notion of statistical (λ, μ)-summability and find its relation with (λ, μ)-statistical convergence. We apply this new method to prove a Korovkin type approximation theorem for functions of two variables. Furthermore, we provide an example in support to show that our result is stronger than the previous ones.
Finite Difference Schemes For Variable Order Time-Fractional First Initial Boundary Value Problems, Gunvant A. Birajdar, M. M. Rashidi
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.
Effect Of Nonlinear Thermal Radiation On Mhd Chemically Reacting Maxwell Fluid Flow Past A Linearly Stretching Sheet, A. M. Ramireddy, J. V. Ramana Reddy, N. Sandeep, V. Sugunamma
Effect Of Nonlinear Thermal Radiation On Mhd Chemically Reacting Maxwell Fluid Flow Past A Linearly Stretching Sheet, A. M. Ramireddy, J. V. Ramana Reddy, N. Sandeep, V. Sugunamma
Applications and Applied Mathematics: An International Journal (AAM)
This communication addresses the influence of nonlinear thermal radiation on magneto hydrodynamic Maxwell fluid flow past a linearly stretching surface with heat and mass transfer. The effects of heat generation/absorption and chemical reaction are taken into account. At first, we converted the governing partial differential equations into nonlinear ordinary differential equations with the help of suitable similarity transformations and solved by using Runge-Kutta based shooting technique. Further, the effects of various physical parameters on velocity, temperature and concentration fields were discussed thoroughly with the help of graphs obtained by using bvp5c MATLAB package. In view of many engineering applications we …
New Structure For Exact Solutions Of Nonlinear Time Fractional Sharma-Tasso-Olver Equation Via Conformable Fractional Derivative, Hadi Rezazadeh, Farid S. Khodadad, Jalil Manafian
New Structure For Exact Solutions Of Nonlinear Time Fractional Sharma-Tasso-Olver Equation Via Conformable Fractional Derivative, Hadi Rezazadeh, Farid S. Khodadad, Jalil Manafian
Applications and Applied Mathematics: An International Journal (AAM)
In this paper new fractional derivative and direct algebraic method are used to construct exact solutions of the nonlinear time fractional Sharma-Tasso-Olver equation. As a result, three families of exact analytical solutions are obtained. The results reveal that the proposed method is very effective and simple for obtaining approximate solutions of nonlinear fractional partial differential equations.
Stability Of Triangular Libration Points In The Sun - Jupiter System Under Szebehely’S Criterion, M. R. Hassan, Md. A. Hassan, M. Z. Ali
Stability Of Triangular Libration Points In The Sun - Jupiter System Under Szebehely’S Criterion, M. R. Hassan, Md. A. Hassan, M. Z. Ali
Applications and Applied Mathematics: An International Journal (AAM)
In the present study, the classical fourth-order Runge-Kutta method with seventh-order automatic step-size control has been carried out to examine the stability of triangular libration points in the Sun-Jupiter system. The Sun is a highly luminous body and Jupiter is a highly spinning body, so radiation pressure of the Sun and oblateness of the Jupiter cannot be neglected. These factors must have some effects on the motion of the infinitesimal mass (spacecraft) and consequent effects on the stability of the triangular libration points. It is to be noted that in our problem, infinitesimal mass exerts no influence of attraction on …
Numerical Simulation Of The Phase Space Of Jupiter-Europa System Including The Effect Of Oblateness, Vinay Kumar, Beena R. Gupta, Rajiv Aggarwal
Numerical Simulation Of The Phase Space Of Jupiter-Europa System Including The Effect Of Oblateness, Vinay Kumar, Beena R. Gupta, Rajiv Aggarwal
Applications and Applied Mathematics: An International Journal (AAM)
We have numerically investigated the phase space of the Jupiter-Europa system in the framework of a Circular Restricted Three-Body Problem. In our model, Jupiter is taken as oblate primary. We have considered time-frequency analysis (TFA) based on wavelets and the Poincare Surface of Section (PSS) for the characterization of orbits in the Jupiter-Europa model. We have exploited both cases: a system with and without considering the effect of oblateness. Graphs (ridge-plots) explaining the phenomenon of resonance trapping, a difference between chaotic sticky orbit and the non-sticky orbit, and periodic and quasi-periodic orbit are presented. Our results of Poincare surfaces of …