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DOI码：10.1007/s00211-020-01115-1

发表刊物：Numerische Mathematik

摘要：In this paper, we study the numerical solution for the singularly perturbed telegraph equation (SPTE) on unbounded domain. Firstly, we investigate the first consistent effective asymptotic expansion for the solution of SPTE by the asymptotic analysis and obtain that the solutions of SPTE have an initial layer near . Next, we introduce the artificial boundaries  to get a finite computational domain  and derive the transparent boundary conditions on  for SPTE. Hence, we can reduce the original problem to an initial-boundary value problem (IBVP) on the bounded domain , and then the equivalence between the original problem and the IBVP on  is proved. In addition, we propose a Crank–Nicolson Galerkin scheme to solve the reduced problem. Furthermore, we use the exponential wave integrator method to deal with the initial layer. We also analyze the stability and convergence of the Crank–Nicolson Galerkin scheme. Finally, some numerical examples validate our theoretical results and show the efficiency and reliability of the transparent boundary conditions and the Crank–Nicolson Galerkin scheme.

论文类型：期刊论文

学科门类：理学

一级学科：数学

文献类型：J

卷号：145

页面范围：345–382

是否译文：否

发表时间：2020-04-03

收录刊物：SCI

通讯作者：黄忠亿