Convergence results of two-step W-methods for two-parameter singular perturbation problems

Two-step W-methods are a class of efficient numerical methods for stiff initial value problems of ordinary differential equations. We study quantitative convergence of parallel two-step W-methods for a class of two-parameter singular perturbation problems, obtain the local and global error estimates for variable stepsizes, show that no order reduction occurs, and extend the corresponding results given by Weiner et al. [R. Weiner, B.A. Schmitt, H. Podhaisky, Two-step W-methods on singular perturbation problems, Report 73, FB Mathematik und Informatik, Universität Marburg, Marburg, 2000].