Legendre Spectral Projection Methods for Hammerstein Integral Equations with Weakly Singular Kernel
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In this paper, we consider the Legendre Galerkin and Legendre collocation methods for solving the Fredholm–Hammerstein integral equation with weakly singular kernels. We evaluate the convergence rates for both the methods in both \(L^2\) and infinity-norm. To improve the convergence rates, iterated Legendre Galerkin and iterated Legendre collocation methods have been considered. We prove that iterated Legendre Galerkin methods converge faster than Legendre Galerkin methods in both \(L^2\) and infinity-norm. Numerical examples are presented to validate the theoretical estimate.
KeywordsHammerstein integral equations Weakly singular kernels Spectral method Galerkin method Collocation method Legendre polynomials
The author takes this opportunity to thank the Reviewers for their valuable suggestions which improve the version of the paper.
- 21.Panigrahi, B.L.: Error analysis of Jacobi spectral collocation methods for Fredholm-Hammerstein integral equations with weakly singular kernel. Int J Comput Math (2018). https://doi.org/10.1080/00207160.2018.1515428