Open Access. Powered by Scholars. Published by Universities.®
Numerical Analysis and Computation Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 9 of 9
Full-Text Articles in Numerical Analysis and Computation
Numerical Studies For Solving Fractional Riccati Differential Equation, N. H. Sweilam, M. M. Khader, A. M. S. Mahdy
Numerical Studies For Solving Fractional Riccati Differential Equation, N. H. Sweilam, M. M. Khader, A. M. S. Mahdy
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, finite difference method (FDM) and Pade'-variational iteration method (Pade'- VIM) are successfully implemented for solving the nonlinear fractional Riccati differential equation. The fractional derivative is described in the Caputo sense. The existence and the uniqueness of the proposed problem are given. The resulting nonlinear system of algebraic equations from FDM is solved by using Newton iteration method; moreover the condition of convergence is verified. The convergence's domain of the solution is improved and enlarged by Pade'-VIM technique. The results obtained by using FDM is compared with Pade'-VIM. It should be noted that the Pade'-VIM is preferable because …
Introducing An Efficient Modification Of The Variational Iteration Method By Using Chebyshev Polynomials, M. M. Khader
Introducing An Efficient Modification Of The Variational Iteration Method By Using Chebyshev Polynomials, M. M. Khader
Applications and Applied Mathematics: An International Journal (AAM)
In this article an efficient modification of the variational iteration method (VIM) is presented using Chebyshev polynomials. Special attention is given to study the convergence of the proposed method. The new modification is tested for some examples to demonstrate reliability and efficiency of the proposed method. A comparison of our numerical results those of the conventional numerical method, the fourth-order Runge-Kutta method (RK4) are given. The comparison shows that the solution using our modification is fast-convergent and is in excellent conformance with the exact solution. Finally, we conclude that the proposed method can be applied to a large class of …
Application Of Differential Transform Method To The Generalized Burgers–Huxley Equation, J. Biazar, F. Mohammadi
Application Of Differential Transform Method To The Generalized Burgers–Huxley Equation, J. Biazar, F. Mohammadi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the differential transform method (DTM) will be applied to the generalized Burgers-Huxley equation, and some special cases of the equation, say, Huxley equation and Fitzhugh-Nagoma equation. The DTM produces an approximate solution for the equation, with few and easy computations. Numerical comparison between differential transform method, Adomian decomposition method and Variational iteration method for Burgers-Huxley, Huxley equation and Fitzhugh-Nagoma equation reveal that differential transform method is simple, accurate and efficient.
Latest Developments In Nonlinear Sciences, Syed T. Mohyud-Din, Ahmet Yildirim
Latest Developments In Nonlinear Sciences, Syed T. Mohyud-Din, Ahmet Yildirim
Applications and Applied Mathematics: An International Journal (AAM)
This paper outlines a detailed study of some latest trends and developments in nonlinear sciences. The major focus of our study will be variational iteration (VIM) and its modifications, homotopy perturbation (HPM), parameter expansion and exp-function methods. The above mentioned schemes are highly accurate, extraordinary efficient, capable to cope with the versatility of the physical problems and are being used to solve a wide class of nonlinear problems. Several examples are given which reveal the justification of our claim.
Modified Variational Iteration Method For Second Order Initial Value Problems, Fazhan Geng
Modified Variational Iteration Method For Second Order Initial Value Problems, Fazhan Geng
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we introduce a modified variational iteration method for second order initial value problems by transforming the integral of iteration process. The main advantages of this modification are that it can overcome the restriction of the form of nonlinearity term in differential equations and improve the iterative speed of conventional variational iteration method. The method is applied to some nonlinear second order initial value problems and the numerical results reveal that the modified method is accurate and efficient for second order initial value problems.
Application Of Homotopy Analysis Method To Fourth-Order Parabolic Partial Differential Equations, M. Matinfar, M. Saeidy
Application Of Homotopy Analysis Method To Fourth-Order Parabolic Partial Differential Equations, M. Matinfar, M. Saeidy
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, by means of the homotopy analysis method (HAM), the solutions of some fourthorder parabolic partial differential equations are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter h that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear examples to obtain the exact solutions. The results reveal that the proposed method is very effective and simple.
A Reliable Approach For Higher-Order Integro-Differential Equations, Muhammad A. Noor, Syed T. Mohyud-Din
A Reliable Approach For Higher-Order Integro-Differential Equations, Muhammad A. Noor, Syed T. Mohyud-Din
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we apply the variational iteration method (VIM) for solving higher-order integro differential equations by converting the problems into system of integral equations. The proposed technique is applied to the re-formulated system of integro-differential equations. Numerical results show the accuracy and efficiency of the suggested algorithm. The fact that the VIM solves nonlinear problems without calculating Adomian’s polynomials is a clear advantage of this technique over the decomposition method.
Solving Higher Dimensional Initial Boundary Value Problems By Variational Iteration Decomposition Method, Muhammad A. Noor, Syed T. Mohyud-Din
Solving Higher Dimensional Initial Boundary Value Problems By Variational Iteration Decomposition Method, Muhammad A. Noor, Syed T. Mohyud-Din
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we apply a relatively new technique which is called the variational iteration decomposition method (VIDM) by combining the traditional variational iteration and the decomposition methods for solving higher dimensional initial boundary value problems. The proposed method is an elegant combination of variational iteration and the decomposition methods. The analytical results of the problems have been obtained in terms of convergent series with easily computable components. The method is quite efficient and is practically well suited for use in these problems. Several examples are given to verify the accuracy and efficiency of the proposed technique.
Variational Iteration Method For Solving Initial And Boundary Value Problems Of Bratu-Type, Muhammad A. Noor, Syed T. Mohyud-Din
Variational Iteration Method For Solving Initial And Boundary Value Problems Of Bratu-Type, Muhammad A. Noor, Syed T. Mohyud-Din
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we present a reliable framework to solve the initial and boundary value problems of Bratu-type which are widely applicable in fuel ignition of the combustion theory and heat transfer. The algorithm rests mainly on a relatively new technique, the variational iteration method. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm.