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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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 417; p. 114537
Main Authors Laib, Hafida, Boulmerka, Aissa, Bellour, Azzeddine, Birem, Fouzia
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.01.2023
Subjects
Collocation method
Error analysis
Taylor polynomials
Two-dimensional Volterra integral equation
65R20
Taylor polynomials
Error analysis
45L05
30K05
34K28
Collocation method
45D05
Two-dimensional Volterra integral equation
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Summary: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