Legendre solutions of integral equations with logarithmic kernels

Abstract

In this paper a finite Legendre expansion is developed to solve linear and nonlinear Volterra integral equations with logarithmic singularities in their kernels. The error analysis is derived. Numerical results and comparisons with other methods in the literature are considered.

Keywords:

• Volterra integral equations
• Integral equations with logarithmic kernels
• Legendre polynomials
• Error analysis
• Numerical approximation of solutions