Shifted fifth-kind Chebyshev Galerkin treatment for linear hyperbolic first-order partial differential equations
| Autor: | G. M. Moatimid, Waleed M. Abd-Elhameed, A. G. Atta, Youssri H. Youssri |
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| Rok vydání: | 2021 |
| Předmět: |
Numerical Analysis
Chebyshev polynomials Partial differential equation Applied Mathematics Linear system MathematicsofComputing_NUMERICALANALYSIS First-order partial differential equation Basis function 010103 numerical & computational mathematics 01 natural sciences Chebyshev filter 010101 applied mathematics Computational Mathematics symbols.namesake Gaussian elimination ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION symbols Applied mathematics 0101 mathematics Galerkin method Mathematics |
| Zdroj: | Applied Numerical Mathematics. 167:237-256 |
| ISSN: | 0168-9274 |
| DOI: | 10.1016/j.apnum.2021.05.010 |
| Popis: | Through the current article, a numerical technique to obtain an approximate solution of one-dimensional linear hyperbolic partial differential equations is implemented. A certain combination of the shifted Chebyshev polynomials of the fifth-kind is used as basis functions. The main idea behind the proposed technique is established on converting the governed boundary-value problem into a system of linear algebraic equations via the application of the spectral Galerkin method. The resulting linear system can be solved by expedients of the Gaussian elimination procedure. The convergence and error analysis of the shifted Chebyshev expansion are carefully investigated. Various numerical examples are given to demonstrate the power and accuracy of the given method. |
| Databáze: | OpenAIRE |
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