Uniform difference method for parameterized singularly perturbed delay differential equations

作者：I. G. Amiraliyeva, Gabil M. Amiraliyev · 发表于：Numerical Algorithms · 年份：2009 · DOI：10.1007/s11075-009-9295-y · 被引用次数：26 · 研究领域：Differential Equations and Numerical Methods、Numerical methods for differential equations、Differential Equations and Boundary Problems

This paper deals with the singularly perturbed initial value problem for quasilinear first-order delay differential equation depending on a parameter. A numerical method is constructed for this problem which involves an appropriate piecewise-uniform meshes on each time subinterval. The difference scheme is shown to converge to the continuous solution uniformly with respect to the perturbation parameter. Some numerical experiments illustrate in practice the result of convergence proved theoretically.