On the numerical solution of weakly singular integral equations of the first kind using a regularized projection method

Abstract

This study investigates a numerical method based on the Jacobi–Gauss quadrature for solving Fredholm integral equations of the first kind with a weakly singular kernel by combining the Tikhonov regularization and projection methods. This numerical method reduces the solution of the weakly singular integral equations of the first kind to the solution of a linear system of algebraic equations. The theoretical analysis of the proposed technique is provided. Finally, several tests are presented to show the validity and efficiency of this approach.

Keywords:

• Ill-posed problems
• Tikhonov regularization
• Legendre polynomials
• Gauss–Jacobi quadrature
• weakly singular integral equations

2010 Mathematics Subject Classifications:

• 45B05
• 65J20
• 65M30

Disclosure statement

No potential conflict of interest was reported by the author(s).