Combined Homotopy and Galerkin Stability Analysis of Mathieu-Like Equations

Solving a System of Linear Equations by Homotopy Analysis Method

‎In this paper‎, ‎an efficient algorithm for solving a system of linear‎ ‎equations based on the homotopy analysis method is presented‎. ‎The‎ ‎proposed method is compared with the classical Jacobi iterative‎ ‎method‎, ‎and the convergence analysis is discussed‎. ‎Finally‎, ‎two‎ ‎numerical examples are presented to show the effectiveness of the‎ ‎proposed method.‎

Homotopy analysis and Homotopy Pad$acute{e}$ methods for two-dimensional coupled Burgers\' equations

In this paper, analytic solutions of two-dimensional coupled Burgers' equations are obtained by the Homotopy analysis and the Homotopy Pad$acute{e}$ methods. The obtained approximation by using Homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by $[m,m]$ Homotopy Pad$acute{e...

Solution and stability analysis of coupled nonlinear Schrodinger equations

We consider a new type of integrable coupled nonlinear Schrodinger (CNLS)equations proposed by our self [submitted to Phys. Plasmas (2011)]. The explicitform of soliton solutions are derived using the Hirota's bilinear method.We show that the parameters in the CNLS equations only determine the regionsfor the existence of bright and dark soliton solutions. Finally, throughthe linear stability an...

Homotopy Analysis Sumudu Transform Method for Nonlinear Equations

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...