A parameter uniform difference scheme for singularly perturbed parabolic delay differential equation with Robin type boundary condition

作者：Selvi P Avudai; Ramanujam N^*

来源：Applied Mathematics and Computation, 2017, 296: 101-115.

DOI：10.1016/j.amc.2016.10.027

• Parabolic differential equations
• Delay
• Singularly perturbed problem
• Finite difference scheme
• Shishkin mesh

A Robin type boundary value problem for a singularly perturbed parabolic delay differential equation is studied on a rectangular domain in the x - t plane. The second-order space derivative is multiplied by a small parameter, which gives rise to parabolic boundary layers on the two lateral sides of the rectangle. A numerical method comprising a standard finite difference scheme on a rectangular piecewise uniform fitted mesh of N-x x N-t elements condensing in the boundary layers is suggested and it is proved to be parameter uniform. More specifically, it is shown that the errors are bounded in the maximum norm by C((Nx-2In2) N-x + N-t(-1)), where C is a constant independent of N-x, N-t and the small parameter. To validate the theoretical result an example is provided.

• 出版日期2017-3-1