A finite difference scheme for strongly coupled systems of singularly perturbed equations

Cheng-Shu You

Department of Applied Mathematics

Feng Chia University

csyou@fcu.edu.tw

    In this talk, we will consider the strongly coupled systems of singularly perturbed convection-diffusion equations, where strong coupling means that the solution components in the system are coupled together through their first derivatives. By decomposing the coefficient matrix of convection term into the Jordan canonical form, we fist construct a so-called Il'in-Allen-Southwell (IAS) scheme for 1D systems and then extend the scheme to 2D systems by employing an alternating direction technique. From the numerical results, we can observe that when the perturbation parameter `\epsilon` is small enough, the developed IAS scheme is fist order convergent in the discrete maximum norm uniformly in `\epsilon` on uniform meshes. This is a joint work with Po-Wen Hsieh and Suh-Yuh Yang.

Keyword: boundary and interior layers, Il'in-Allen-Southwell scheme, singularly perturbed convection-diffusion equation, strongly coupled system, uniform convergence.