A Novel Wavelet-based Approximation Scheme for the Approximate Solution/Source of Fredholm Integral Equation of the Second Kind with Variable Coefficient and the Pseudo-Logarithmic Kernels
Sudam Bin
Department of Mathematics, Visva-Bharati (A Central University), Santiniketan–731235, West Bengal, India.
Sharda Kumari
Department of Mathematics, Visva-Bharati (A Central University), Santiniketan–731235, West Bengal, India.
Madan Mohan Panja *
Department of Mathematics, Visva-Bharati (A Central University), Santiniketan–731235, West Bengal, India.
*Author to whom correspondence should be addressed.
Abstract
This study introduces an efficient orthonormal polynomial wavelet-based approximation scheme for solving Fredholm integral equations of the second kind with logarithmic/pseudo-logarithmic singular kernels. The method exhibits high accuracy and computational efficiency and seems applicable simultaneously when the exact solution or the source term is unknown to be determined. The examples tested here validate the accuracy and effectiveness of the scheme proposed here.
Keywords: Fredholm integral equation, pseudo-logarithmic singular kernel, orthonormal polynomial wavelet basis, sinh-tanh quadrature formula