Theoretical and numerical analysis of a first-kind linear Volterra functional integral equation with weakly singular kernel and vanishing delay.

Autor:	Naghdi, Niloofar, Shahmorad, Sedaghat
Předmět:	VOLTERRA equations NUMERICAL analysis PROBLEM solving LINEAR statistical models POLYNOMIALS
Zdroj:	Numerical Algorithms; Sep2024, Vol. 97 Issue 1, p453-473, 21p
Abstrakt:	In this study, we investigate the existence and uniqueness of a solution for a first-kind linear Volterra functional integral equation with proportional delay and weakly singular kernel, which has been stated as a research problem by H. Brunner (2017, pp. 99–100). We solve the problem numerically by the Tau-collocation method using Müntz-Jacobi polynomials along with the Gauss-Jacobi quadrature rule. Moreover, we prove a convergence theorem for the proposed method in L 2 -norm. We use several examples to corroborate the theoretical results and numerical efficiency of the method. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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