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- Title
Convergence analysis of a Legendre spectral collocation method for nonlinear Fredholm integral equations in multidimensions.
- Authors
Zaky, Mahmoud A.; Hendy, Ahmed S.
- Abstract
It is a very challenging task to solve a nonlinear integral equation in multidimensions. The main purpose of this paper is to develop and analyze a spectral collocation method for a class of nonlinear Fredholm integral equations of the second kind in multidimensions. The proposed spectral collocation method is based on a multivariate Legendre approximation in the frequency space. It is shown by both theory and numerics that the proposed spectral collocation scheme not only significantly reduces the number of degrees of freedom but also produces very accurate approximations.
- Subjects
NONLINEAR integral equations; FREDHOLM equations; INTEGRAL equations; DEGREES of freedom; COLLOCATION methods
- Publication
Mathematical Methods in the Applied Sciences, 2024, Vol 47, Issue 13, p10717
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.6443