The Lanczos-Chebyshev Pseudospectral Method for Solution of Differential Equations
| Autor: | Peter Y. P. Chen |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Physics::Computational Physics
Chebyshev polynomials 010102 general mathematics Mathematical analysis Chebyshev iteration General Medicine 01 natural sciences Chebyshev filter Mathematics::Numerical Analysis 010101 applied mathematics Gauss pseudospectral method Chebyshev pseudospectral method Applied mathematics Pseudospectral optimal control 0101 mathematics Chebyshev nodes Chebyshev equation Mathematics |
| Zdroj: | Applied Mathematics. :927-938 |
| ISSN: | 2152-7393 2152-7385 |
| Popis: | In this paper, we propose to replace the Chebyshev series used in pseudospectral methods with the equivalent Chebyshev economized power series that can be evaluated more rapidly. We keep the rest of the implementation the same as the spectral method so that there is no new mathematical principle involved. We show by numerical examples that the new approach works well and there is indeed no significant loss of solution accuracy. The advantages of using power series also include simplicity in its formulation and implementation such that it could be used for complex systems. We investigate the important issue of collocation point selection. Our numerical results indicate that there is a clear accuracy advantage of using collocation points corresponding to roots of the Chebyshev polynomial. |
| Databáze: | OpenAIRE |
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