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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 …
Validation Of The A Posteriori Error Estimator Based On Polynomial Preserving Recovery For Linear Elements, Zhimin Zhang, Ahmed Naga
Validation Of The A Posteriori Error Estimator Based On Polynomial Preserving Recovery For Linear Elements, Zhimin Zhang, Ahmed Naga
Mathematics Research Reports
In this paper the quality of the error estimator based on the Polynomial Preserving Recovery (PPR) is investigated using the computer-based approach proposed by Babiiska et al. A comparison is made between the error estimator based on the PPR and the one based on the Superconvergence Patch Recovery (SPR). It was found that the PPR is at least as good as the SPR.