摘要

The theory of the Adomian modified decomposition method (AMDM) for solving linear and nonlinear differential equations is well established. However, the solutions obtained by using the current AMDM are valid only for a very small region. In this paper, a new aftertreatment technique is proposed to improve the accuracy of the AMDM during a wide region. Based on the proposed aftertreatment technique, the truncated series solution obtained by the AMDM can be expressed as another series in terms of the independent sine and cosine trigonometric functions. Two numerical examples are presented and compared to those obtained from the numerical 4th-order Runge-Kutta algorithm. It is shown that the AMDM with the proposed aftertreatment technique offers an accurate and effective method for solving nonlinear differential equations in a wide applicable region.

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