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Nonlinear differential equations; the homotopy deform method; the simplified reproducing kernel method; Adomian decomposition method.

In this paper, the combination of homotopy deform method (HDM) and simplified reproducing kernel method (SRKM) is introduced for solving the boundary value problems (BVPs) of nonlinear differential equations. The solution methodology is based on Adomian decomposition and reproducing kernel method (RKM). By the HDM, the nonlinear equations can be converted into a series of linear BVPs. After that, the simplified reproducing kernel method, which not only facilitates the reproducing kernel but also avoids the time-consuming Schmidt orthogonalization process, is proposed to solve linear equations. Some numerical test problems including ordinary differential equations and partial differential equations are analysed to illustrate the procedure and confirm the performance of the proposed method. The results faithfully reveal that our algorithm is considerably accurate and effective as expected.

MIN-QIANG XU¹ YING-ZHEN LIN¹

1. School of Science, Zhuhai Campus, Beijing Institute of Technology, Zhuhai, Guangdong, 519085, People’s Republic of China

Published

16 October 2016

Manuscript received

11 September 2015

Manuscript revised

15 October 2015

Accepted

16 December 2015

Early published

23 September 2016