A natural boundary element method for the Sobolev equation in the 2D unbounded domain

Boundary value problems

Jing Yang¹  Fei Teng¹  Zhendong Luo² 

[1] School of Control and Computer Engineering, North China Electric Power University, Beijing, China;School of Mathematics and Physics, North China Electric Power University, Beijing, China

关键词: natural boundary element method;    Sobolev equation;    error estimate;    numerical experiment;    65N30;    35Q10;   

DOI  :  10.1186/s13661-017-0910-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, we devote ourselves to establishing a natural boundary element (NBE) method for the Sobolev equation in the 2D unbounded domain. To this end, we first constitute the time semi-discretized super-convergence format for the Sobolev equation by means of the Newmark method. Then, using the principle of natural boundary reduction, we establish a fully discretized NBE format based on the natural integral equation and the Poisson integral formula of this problem and analyze the errors between the exact solution and the fully discretized NBE solutions. Finally, we use some numerical experiments to verify that the NBE method is effective and feasible for solving the Sobolev equation in the 2D unbounded domain.

【 授权许可】

CC BY