Homotopy deform method for reproducing kernel space for nonlinear boundary value problems

Pramana

YING-ZHEN LIN¹  MIN-QIANG XU¹ 

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

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

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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.

【 授权许可】

Unknown