Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
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 …