Revised adomain decomposition method for finding all solutions of nonlinear equations and system of nonlinear equations
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In this paper, we approximate the real and complex roots of non-linear equations and system of non-linear equations. For this purpose, by using the convergence conditions of Adomian decomposition method (ADM) for solving functional equations, two predictor-corrector algorithms are presented. First algorithm can approximate the real and complex roots of non-linear equations,whereas the existing ADMs can only obtain real solutions. Second algorithm can find the solutions of a system of non-linear equations, such that the proposed algorithm is more efficient than existing ADMs. Some examples are presented to illustrate the algorithms. In addition, it will be shown that the proposed method can compute suitable approximate real and complex roots of a given function more efficient than Maple software and one is able to converge to a solution of given system faster than traditional ADMs.
Abstract
In this paper, we approximate the real and complex roots of non-linear equations and system of non-linear equations. For this purpose, by using the convergence conditions of Adomian decomposition method (ADM) for solving functional equations, two predictor-corrector algorithms are presented. First algorithm can approximate the real and complex roots of non-linear equations,whereas the existing ADMs can only obtain real solutions. Second algorithm can find the solutions of a system of non-linear equations, such that the proposed algorithm is more efficient than existing ADMs. Some examples are presented to illustrate the algorithms. In addition, it will be shown that the proposed method can compute suitable approximate real and complex roots of a given function more efficient than Maple software and one is able to converge to a solution of given system faster than traditional ADMs.
참고문헌 (16)
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