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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-22 2:08 |
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Conference: Bucharest University Faculty of Physics 2007 Meeting
Section: Theoretical Physics and Applied Mathematics Seminar
Title:
Numerical solutions for linear ODE and PDE with Dirichlet boundary conditions using modified weighted residues in Chebyshev collocation points
Authors:
Prof. dr. S. Spanulescu
Affiliation:
Department of Physics, Hyperion University of Bucharest
Department of Physics, University of Bucharest
E-mail
Keywords:
Abstract:
A new method for numerically solving second order linear ODE and PDE with Dirichlet boundary conditions is presented. Comparison with some standard methods as Galerkin, spectral, pseudo spectral and classical Clenshaw and Curtis Chebyshev matrix approximations is made. It follows that for larger domains of integration, the main difficulty for these methods resides in the ill-conditioned system of linear equations, which limits the accuracy of the results. The bad condition number of the matrix is due to the narrow domain of orthogonality of the usually eligible polinoms. The new method uses an additional integration that performs an overall smoothing of the residue and decreases the matrix condition number. In addition, it seems that the Gauss-Lobatto sampling method fails to cover larger domains, so it should be replaced by explicitly introducing the boundary conditions in the weighted residue. Some examples of linear ODE with boundary conditions showed errors significantly smaller (sometimes within a 10^-5 ratio) than the known methods, if the interval is larger than [-1,1]
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