Galerkin methods for a singularly perturbed hyperbolic problem with nonlocal nonlinearity
| Autor: | Elizabeth Greenwell Yanik, Benjamin F. Esham |
|---|---|
| Jazyk: | angličtina |
| Předmět: |
Partial differential equation
Mathematical analysis Computational Mathematics Nonlinear system Computational Theory and Mathematics Modelling and Simulation Modeling and Simulation Time derivative Initial value problem Boundary value problem Asymptotic expansion Galerkin method Hyperbolic partial differential equation Mathematics |
| Zdroj: | Computers & Mathematics with Applications. (2):1-22 |
| ISSN: | 0898-1221 |
| DOI: | 10.1016/0898-1221(91)90038-6 |
| Popis: | We consider the numerical approximation of hyperbolic and parabolic problems with nonlocal nonlinearity by Galerkin methods, and provide optimal order L 2 error estimates in the continuous-time case. Three-level discrete schemes are then introduced and used to investigate the relationship between a singularly perturbed hyperbolic problem with small parameter ϵ 2 multiplying the highest time derivative and the reduced problem of parabolic type. For small ϵ 2 , the problem of stiffness in the hyperbolic problem can be avoided by utilizing the solution of the reduced problem in accordance with a recent asymptotic result of Esham and Weinacht. The advantage of using a two-term asymptotic expansion is also briefly considered. |
| Databáze: | OpenAIRE |
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