Uniformly convergent difference schemes for a singularly perturbed third order boundary value problem

作者：Roos Hans Goerg; Teofanov Ljiljana^*; Uzelac Zorica

来源：Applied Numerical Mathematics, 2015, 96: 108-117.

DOI：10.1016/j.apnum.2015.06.002

• Singular perturbation
• Boundary value problem
• Layer-adapted meshes
• Finite difference method

In this paper we consider a numerical approximation of a third order singularly perturbed boundary value problem by an upwind finite difference scheme on a Shishkin mesh. The behavior of the solution, and the stability of the continuous problem are discussed. The proof of the uniform convergence of the proposed numerical method is based on the strongly uniform stability and a weak consistency property of the discrete problem. Numerical experiments verify our theoretical results.

• 出版日期2015-10