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

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Abstract

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.

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Authors and Affiliations

  1. Graduate School of Information Sciences, Hiroshima City University, 3-4-1, Ozuka-higashi, Asaminami-ku, Hiroshima, 731-3194, Japan

    Tomoaki Okayama

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  1. Tomoaki Okayama
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Correspondence to Tomoaki Okayama.

Additional information

Communicated by Lothar Reichel.

This work was partially supported by JSPS KAKENHI Grant Number JP17K14147.

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Okayama, T. Theoretical analysis of Sinc-collocation methods and Sinc-Nyström methods for systems of initial value problems. Bit Numer Math 58, 199–220 (2018). https://doi.org/10.1007/s10543-017-0663-z

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  • DOI: https://doi.org/10.1007/s10543-017-0663-z

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