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

• Autorzy: Torabi Seyed Mousa , Tari Abolfazl , Shahmorad Sedaghat

Identyfikatory

DOI

10.1515/jaa-2019-0001

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

two-dimensional nonlinear Volterra integral equations; integral equations of the second kind; two-step collocation methods

PL

równanie całkowe Volterry dwuwymiarowe nieliniowe; równania całkowe drugiego rodzaju; metoda kolokacji dwuetapowa

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2019
• Tom: Vol. 25, nr 1
• Strony: 1--11
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Torabi Seyed Mousa

• Department of Mathematics, Shahed University, Tehran, Iran

autor

Tari Abolfazl

• Department of Mathematics, Shahed University, Tehran, Iran

autor

Shahmorad Sedaghat

• Faculty of Mathematical Science, University of Tabriz, Tabriz, Iran

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).