Solving initial value problems by residual power series method

Abstract

In this article, the residual power series method for solving first-order initial value problems is introduced. The new method provides the solution in the form of a power series with easily computable components using Maple13 software package. The proposed method obtains Maclaurin expansion of the solution and reproduces the exact solution when the solution is polynomial. The proposed technique is applied to several test examples to illustrate the accuracy, efficiency, and applicability of the method.

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