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Partial Differential Equations Commons™
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Articles 1 - 7 of 7
Full-Text Articles in Partial Differential Equations
(R2074) A Comparative Study Of Two Novel Analytical Methods For Solving Time-Fractional Coupled Boussinesq-Burger Equation, Jyoti U. Yadav, Twinkle R. Singh
(R2074) A Comparative Study Of Two Novel Analytical Methods For Solving Time-Fractional Coupled Boussinesq-Burger Equation, Jyoti U. Yadav, Twinkle R. Singh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a comparative study between two different methods for solving nonlinear timefractional coupled Boussinesq-Burger equation is conducted. The techniques are denoted as the Natural Transform Decomposition Method (NTDM) and the Variational Iteration Transform Method (VITM). To showcase the efficacy and precision of the proposed approaches, a pair of different numerical examples are presented. The outcomes garnered indicate that both methods exhibit robustness and efficiency, yielding approximations of heightened accuracy and the solutions in a closed form. Nevertheless, the VITM boasts a distinct advantage over the NTDM by addressing nonlinear predicaments without recourse to the application of Adomian polynomials. …
A Comparative Study Of Shehu Variational Iteration Method And Shehu Decomposition Method For Solving Nonlinear Caputo Time-Fractional Wave-Like Equations With Variable Coefficients, Ali Khalouta, Abdelouahab Kadem
A Comparative Study Of Shehu Variational Iteration Method And Shehu Decomposition Method For Solving Nonlinear Caputo Time-Fractional Wave-Like Equations With Variable Coefficients, Ali Khalouta, Abdelouahab Kadem
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a comparative study between two different methods for solving nonlinear Caputo time-fractional wave-like equations with variable coefficients is conducted. These two methods are called the Shehu variational iteration method (SVIM) and the Shehu decomposition method (SDM). To illustrate the efficiency and accuracy of the proposed methods, three different numerical examples are presented. The results obtained show that the two methods are powerful and efficient methods which both give approximations of higher accuracy and closed form solutions if existing. However, the SVIM has an advantage over SDM that it solves the nonlinear problems without using the Adomian polynomials. …
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.
The He's Variational Iteration Method For Solving The Integro-Differential Parabolic Problem With Integral Conditions, Saeid Abbasbandy, Hadi R. Ghehsareh
The He's Variational Iteration Method For Solving The Integro-Differential Parabolic Problem With Integral Conditions, Saeid Abbasbandy, Hadi R. Ghehsareh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the variational iteration method is applied for finding the solution of an Integro-differential parabolic problem with integral conditions. Convergence of the proposed method is also discussed. Finally, some numerical examples are given to show the effectiveness of the proposed method.
Variational Iteration Method For Solving Two-Parameter Singularly Perturbed Two Point Boundary Value Problem, Marwan Taiseer Alquran, Nurettin Doğan
Variational Iteration Method For Solving Two-Parameter Singularly Perturbed Two Point Boundary Value Problem, Marwan Taiseer Alquran, Nurettin Doğan
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, He’s Variational iteration method (VIM) is used for the solution of singularly perturbed two-point boundary value problems with two small parameters multiplying the derivatives. Some problems are solved to demonstrate the applicability of the method. This paper suggests a patern for choosing the freely selected initial approximation in the VIM that leads to a very well approximation by only one iteration.