Tau approximate solution of weakly singular Volterra integral equations with Legendre wavelet basis

ABSTRACT

In this paper, a spectral Tau method based on Legendre Wavelet basis is proposed. For this purpose we present a stable operational Tau method based on Legendre Wavelet basis. This method provides an efficient approximate solution for weakly singular Volterra integral equations by using reduced set of matrix operations. An error estimation of the Tau method is also introduced. Finally we demonstrate the validity and applicability of the method by numerical examples.

KEYWORDS:

• Weakly singular volterra integral equations
• tau method
• legendre wavelet basis
• error estimation

2010 AMS SUBJECT CLASSIFICATIONS:

• 45B05
• 74G10

Disclosure statement

No potential conflict of interest was reported by the authors.