Study on how to resolve the boundary value problem of three-region composite Thomson equation

Article type: Research Article

Authors: Wang, Yong^a | Dong, Xiaoxu^{b; *} | Li, Shunchu^a

Affiliations: [a] School of Science, Xihua University, Chengdu, Sichuan, China | [b] School of Science, Southwest Petroleum University, Chengdu, Sichuan, China

Correspondence: [*] Corresponding author: Xiaoxu Dong, School of Science, Southwest Petroleum University, Chengdu, Sichuang 610500, China. Tel.: +86 18228021140; E-mail:[email protected]

Abstract: On the basis of the theory in similar structure of solution of the boundary value problem for a differential equation, this paper studies the boundary value problem of a three-region composite, Thomson equation. Firstly, this paper obtains similar structure related to solution of the boundary value problem of a three-region composite Thomson equation. Secondly, this paper points out the steps and flow chart about the algorithm for solving the boundary value problem. Finally, this paper gives an application of the obtained steps and draws the solution curve of the boundary value problem by executing the program on the computer. The obtained steps mentioned in this paper are not only simple and effective to resolve the complicated boundary value problem of a differential equation, but also useful to acquire the analytical solution of the model of composite reservoir.

Keywords: Boundary value problem, three-region composite Thomson equation, similar constructing method, similar kernel function, function of guide solution

DOI: 10.3233/JCM-160606

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 16, no. 1, pp. 111-124, 2016