Variational iteration method for autonomous ordinary differential systems
Applied Mathematics and Computation
Advanced Engineering Mathematics: Maple Computer Guide
Advanced Engineering Mathematics: Maple Computer Guide
A comparison between the variational iteration method and Adomian decomposition method
Journal of Computational and Applied Mathematics
Variational iteration method-Some recent results and new interpretations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Numerical approach to differential equations of fractional order
Journal of Computational and Applied Mathematics
On the convergence of He's variational iteration method
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Improvement of He's variational iteration method for solving systems of differential equations
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Reliable approaches of variational iteration method for nonlinear operators
Mathematical and Computer Modelling: An International Journal
Hi-index | 7.29 |
The variational iteration method and the homotopy analysis method, as alternative methods, have been widely used to handle linear and nonlinear models. The main property of the methods is their flexibility and ability to solve nonlinear equations accurately and conveniently. This paper deals with the numerical solutions of nonlinear fractional differential equations, where the fractional derivatives are considered in Caputo sense. The main aim is to introduce efficient algorithms of variational iteration and homotopy analysis methods that can be simply used to deal with nonlinear fractional differential equations. In these algorithms, Legendre polynomials are effectively implemented to achieve better approximation for the nonhomogeneous and nonlinear terms that leads to facilitate the computational work. The proposed algorithms are capable of reducing the size of calculations, improving the accuracy and easily overcome the difficulty arising in calculating complicated integrals. Numerical examples are examined to show the efficiency of the algorithms.