Numerical treatment of nonlocal boundary value problem with layer behaviour

作者：Cimen Erkan^*; Cakir Musa

来源：Bulletin of the Belgian Mathematical Society Simon Stevin, 2017, 24(3): 339-352.

DOI：10.36045/bbms/1506477685

• Singular perturbation
• nonlocal condition
• finite difference method
• initial layer
• uniform convergence

This paper deals with the singularly perturbed nonlocal boundary value problem for a linear first order differential equation. For the numerical solution of this problem, we use a fitted difference scheme on a piecewise uniform Shishkin mesh. An error analysis shows that the method is almost first order convergent, in the discrete maximum norm, independently of the perturbation parameter. Numerical results are presented which illustrate the theoretical results.

• 出版日期2017-9