Spectral Methods for Volterra Integral Equations

Mahesh Boda; V. Dharmaiah

doi:https://doi.org/10.14445/22315373/IJMTT-V41P501

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 41 | Number 1 | Year 2017 | Article Id. IJMTT-V41P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V41P501

Spectral Methods for Volterra Integral Equations

Mahesh Boda, V. Dharmaiah

Citation :

Mahesh Boda, V. Dharmaiah, "Spectral Methods for Volterra Integral Equations," International Journal of Mathematics Trends and Technology (IJMTT), vol. 41, no. 1, pp. 1-8, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V41P501

Abstract

The purpose of this paper is to introduce a novel numerical method called a legedre-collocation method to solve the Volterra integral equations of second kind. We also provide error analysis for the proposed method, which indicates that the numerical errors decay exponentially provided that the kernel function and the source function are sufficiently smooth. Numerical results confirm theoretical prediction of the exponential rate of convergence.

Keywords

Volterra integral equations of the second kind, Legendre-collocation method Convergence analysis.

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