Numerical solution of two-dimensional linear and nonlinear Volterra integral equations using Taylor collocation method

Numerical solution of two-dimensional linear and nonlinear Volterra integral equations using Taylor collocation method

The main purpose of this work is to provide a numerical approach for two-dimensional Volterra integral equations (2D-VIEs). An algorithm based on the use of Taylor polynomials is developed to construct a collocation solution v∈Sp−1,p−1(−1)(ΠN,M) for approximating the solution of 2D-VIEs. It is shown...

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Veröffentlicht in:Journal of computational and applied mathematics 2023-01, Vol.417, p.114537, Article 114537
Hauptverfasser: Laib, Hafida, Boulmerka, Aissa, Bellour, Azzeddine, Birem, Fouzia
Format: Artikel
Sprache:eng
Schlagworte:
Collocation method
Error analysis
Taylor polynomials
Two-dimensional Volterra integral equation
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Zusammenfassung:The main purpose of this work is to provide a numerical approach for two-dimensional Volterra integral equations (2D-VIEs). An algorithm based on the use of Taylor polynomials is developed to construct a collocation solution v∈Sp−1,p−1(−1)(ΠN,M) for approximating the solution of 2D-VIEs. It is shown that this algorithm is convergent. Some numerical examples are included to demonstrate the accuracy of the presented method.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2022.114537