Abstract
In this paper, efficient modification of Adomain decomposition method is proposed to solve nonlinear partial differential equations. Yields solution in rapid convergent series from easily computable terms to get exact solution, and yields in few iterations we get exact solution. Moreover, this modification does not require any linearization, discretization, or perturbations and therefore reduces the computations. Two illustration examples are introduced and illustrate the procedure of modification is simple yet highly accurate and rapidly converge to exact solution compares with the ADM or other modifications. The methodology presented here is useful for strongly nonlinear problems.
Highlights
In the last three decades, the Adomian Decomposition Method (ADM) has confirmed successful in getting analytical solution of non-linear differential equations by obtained solution in terms of convergent power series [1]
Achouri and Omrani [10], applied the ADM to get numerical solutions for the damped gener alized regularized long-wave equation (DGRLW) with variable coefficients, and Tawfiq et al [11,12,13,14] used this method for solving different model equations
It is seen that suggested modification has the same exact solution
Summary
In the last three decades, the Adomian Decomposition Method (ADM) has confirmed successful in getting analytical solution of non-linear differential equations by obtained solution in terms of convergent power series [1]. This method does not require discretization of the variables or domain [2, 3]. There has been development in the application of ADM in solving partial differential equations (PDEs) with variable coefficients.
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