Application of Numerical Iterative Methods for Solving Benjamin-Bona-Mahony Equation
Subject Areas : Journal of Computer & Robotics
Shadan
Sadigh behzadi
1
(Department of Mathematics Islamic Azad University Qazvin Branch, Qazvin, Iran)
Keywords: Homotopy Analysis Method, Variational Iteration Method, Adomian decomposition method, Generalized Benjamin-Bona-Mahony equation, Modified Adomian decomposition method, Modified variational iteration method,
Abstract :
In this paper, a generalized Benjamin-Bona-Mahony equation ( BBM)is solved by using the Adomian's decomposition method (ADM) ,modified Adomian's decomposition method (MADM), variationaliteration method (VIM), modified variational iteration method (MVIM)and homotopy analysis method (HAM). The approximate solution of thisequation is calculated in the form of series which its componentsare computed by applying a recursive relation. The existence anduniqueness of the solution and the convergence of the proposedmethods are proved. A numerical example is studied to demonstratethe accuracy of the presented methods.The MVIM has been shown to solve effectively, easily and accuratelya large class of nonlinear problems with the approximations whichconvergent are rapidly to exact solutions.
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