Modified Legendre rational and exponential collocation methods for solving nonlinear Hammerstein integral equations on the semi-infinite domain

Abstract

This paper discusses two efficient collocation methods for solving the Hammerstein integral equations on the semi-infinite domain, where the underlying solutions decay to zero at infinity. These methods are based upon modified Legendre rational and exponential functions, and reduce the Hammerstein integral equation to a nonlinear algebraic system. The error between the approximate and exact solutions in the usual $L^2$-norm is estimated. Finally, some numerical experiments are presented to examine and demonstrate the effectiveness and accuracy of the proposed methods in comparison to other approaches.

Keywords:

• Hammerstein integral equations
• semi-infinite domain
• modified Legendre rational functions
• modified Legendre exponential functions
• Collocation method

2020 AMS Subject Classifications:

• 45B05
• 65R20
• 34K28

Acknowledgements

The authors are very grateful to the editor and anonymous referees for their valuable comments, which greatly enhanced the quality of the paper.

Disclosure statement

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