Error analysis of Jacobi spectral collocation methods for Fredholm-Hammerstein integral equations with weakly singular kernel

ABSTRACT

The Jacobi spectral collocation method is being proposed to solve Fredholm-Hammerstein integral equations with the weakly singular kernel and smooth solutions. By using the appropriate quadrature rule, the integral operator is approximated by the discrete operator, which gives rise to the Jacobi collocation method for Fredholm-Hammerstein integral equations with the weakly singular kernel. The convergence analysis for the approximated solution with the exact solution is being discussed for both weighted $L^2$-norm and infinity-norm. Numerical examples are presented to validate the theoretical estimate.

KEYWORDS:

• Fredholm-Hammerstein integral equations
• weakly singular kernels
• sepctral methods
• Jacobi collocation methods
• convergence analysis

2010 MSC SUBJECT CLASSIFICATIONS:

• 45G05
• 65R20

Disclosure statement

No potential conflict of interest was reported by the author.