Modified Legendre rational and exponential collocation methods for solving nonlinear Hammerstein integral equations on the semi-infinite domain. (English) Zbl 1524.65980
Summary: 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 methodReferences:
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