Linss, Torsten; Madden, Niall Analysis of an alternating direction method applied to singularly perturbed reaction-diffusion problems. (English) Zbl 1195.65119 Int. J. Numer. Anal. Model. 7, No. 3, 507-519 (2010). Summary: We present an analysis of an alternating direction implicit (ADI) scheme for a linear, singularly perturbed reaction-diffusion equation. By providing an expression for the error that separates the temporal and spatial components, we can use existing results for steady-state problems to give a succinct analysis for the time-dependent problem, and that generalizes for various layer-adapted meshes. We report the results of numerical experiments that support the theoretical findings. In addition, we provide a numerical comparison between the ADI and Euler techniques, as well details of the computational advantage gained by parallelizing the algorithm. Cited in 17 Documents MSC: 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 35K20 Initial-boundary value problems for second-order parabolic equations 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35B25 Singular perturbations in context of PDEs 65F10 Iterative numerical methods for linear systems 65M20 Method of lines for initial value and initial-boundary value problems involving PDEs Keywords:reaction-diffusion problems; layer-adapted meshes; alternating directions; singular perturbation; alternating direction implicit scheme; numerical experiments × Cite Format Result Cite Review PDF Full Text: Link