A uniformly convergent alternating direction HODIE finite difference scheme for 2D time-dependent convection-diffusion problems. (English) Zbl 1118.65092
A finite-difference scheme for a class of convection-diffusion problems in 2D space is presented and analyzed. The problem under consideration is a singularly-perturbed time-dependent partial differential equations problem with convection term positive in both space directions, and a nonnegative reaction term. The proposed method is uniformly convergent with respect to diffusion parameter, and reaches almost second-order precision in space. The authors argue that the developed method is applicable to a wider class of problems than the method is originally designed for.
Reviewer: Alexei Cheviakov (Vancouver)
MSC:
65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
35K15 | Initial value problems for second-order parabolic equations |
35B25 | Singular perturbations in context of PDEs |