Startseite Two-step collocation methods for two-dimensional Volterra integral equations of the second kind
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Two-step collocation methods for two-dimensional Volterra integral equations of the second kind

  • Seyed Mousa Torabi , Abolfazl Tari EMAIL logo und Sedaghat Shahmorad
Veröffentlicht/Copyright: 21. Mai 2019

Abstract

In this paper, we develop two-step collocation (2-SC) methods to solve two-dimensional nonlinear Volterra integral equations (2D-NVIEs) of the second kind. Here we convert a 2D-NVIE of the second kind to a one-dimensional case, and then we solve the resulting equation numerically by two-step collocation methods. We also study the convergence and stability analysis of the method. At the end, the accuracy and efficiency of the method is verified by solving two test equations which are stiff. In examples, we use the well-known differential transform method to obtain starting values.

MSC 2010: 65R20

Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments that helped the authors to improve the paper.

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Received: 2018-01-03
Revised: 2018-02-27
Accepted: 2018-04-12
Published Online: 2019-05-21
Published in Print: 2019-06-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 21.11.2025 von https://www.degruyterbrill.com/document/doi/10.1515/jaa-2019-0001/html
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