Theoretical analysis of Sinc-collocation methods and Sinc-Nystrom methods for systems of initial value problems

摘要

A Sinc-collocation method was proposed by Stenger, who also gave a theoretical analysis of the method in the case of a "scalar" equation. This paper extends the theoretical results to the case of a "system" of equations. Furthermore, this paper proposes a more efficient method by replacing the variable transformation employed in Stenger's method. The efficiency was confirmed by both a theoretical analysis and some numerical experiments. In addition to the existing and newly proposed Sinc-collocation methods, this paper also gives similar theoretical results for the Sinc-Nystrom methods proposed by Nurmuhammad et al. In terms of computational cost, the newly proposed Sinc-collocation method is the most efficient among these methods.