Triangular functions in solving Weakly Singular Volterra integral equations

Year 2023, Volume: 7 Issue: 1, 195 - 204, 31.03.2023

Monireh Nosrati Hojjat Afshari

https://doi.org/10.31197/atnaa.1236577

Abstract

In this paper, we propose the triangular orthogonal functions as a basis functions
for solution of weakly singular Volterra integral equations of the second
kind. Powerful properties of these functions and some operational matrices
are utilized in a direct method to reduce singular integral equation to
some algebraic equations. The presented method does not need any integration
for obtaining the constant coefficients. The method is computationally
attractive, and applications are demonstrated through illustrative examples.

Keywords

triangular functions, Abel integral equation, operational matrices, error analysis, triangular functions, Abel integral equation, operational matrices,, error analysis

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