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Full-Text Articles in Physical Sciences and Mathematics
Superconvergence Of Iterated Solutions For Linear And Nonlinear Integral Equations: Wavelet Applications, Boriboon Novaprateep
Superconvergence Of Iterated Solutions For Linear And Nonlinear Integral Equations: Wavelet Applications, Boriboon Novaprateep
Mathematics & Statistics Theses & Dissertations
In this dissertation, we develop the Petrov-Galerkin method and the iterated Petrov-Galerkin method for a class of nonlinear Hammerstein equation. We also investigate the superconvergence phenomenon of the iterated Petrov-Galerkin and degenerate kernel numerical solutions of linear and nonlinear integral equations with a class of wavelet basis. The Fredholm integral equations and the Hammerstein equations are considered in linear and nonlinear cases respectively. Alpert demonstrated that an application of a class of wavelet basis elements in the Galerkin approximation of the Fredholm equation of the second kind leads to a system of linear equations which is sparse. The main concern …
Superconvergence In Iterated Solutions Of Integral Equations, Peter A. Padilla
Superconvergence In Iterated Solutions Of Integral Equations, Peter A. Padilla
Mathematics & Statistics Theses & Dissertations
In this thesis, we investigate the superconvergence phenomenon of the iterated numerical solutions for the Fredholm integral equations of the second kind as well as a class of nonliner Hammerstein equations. The term superconvergence was first described in the early 70s in connection with the solution of two-point boundary value problems and other related partial differential equations. Superconvergence in this context was understood to mean that the order of convergence of the numerical solutions arising from the Galerkin as well as the collocation method is higher at the knots than we might expect from the numerical solutions that are obtained …