Theoretical analysis of Sinc-collocation methods and Sinc-Nyström methods for systems of initial value problems
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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-Nyström methods proposed by Nurmuhammad et al. In terms of computational cost, the newly proposed Sinc-collocation method is the most efficient among these methods.
KeywordsSinc approximation Sinc indefinite integration Differential equation Volterra integral equation tanh transformation Double-exponential transformation
Mathematics Subject Classification65L05 65R20 65D30
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