Conservative finite difference scheme for the nonlinear fourth-order wave equation
| Autor: | Talha Achouri |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
0209 industrial biotechnology
Applied Mathematics Finite difference 020206 networking & telecommunications 02 engineering and technology Wave equation Computational Mathematics Nonlinear system 020901 industrial engineering & automation Norm (mathematics) Bounded function 0202 electrical engineering electronic engineering information engineering Finite difference scheme Applied mathematics Uniqueness Brouwer fixed-point theorem Mathematics |
| Zdroj: | Applied Mathematics and Computation. 359:121-131 |
| ISSN: | 0096-3003 |
| DOI: | 10.1016/j.amc.2019.04.033 |
| Popis: | A conservative finite difference scheme is presented for solving the two-dimensional fourth-order nonlinear wave equation. The existence of the numerical solution of the finite difference scheme is proved by Brouwer fixed point theorem. With the aid of the fact that the discrete energy is conserved, the finite difference solution is proved to be bounded in the discrete L ∞ − norm. Then, the difference solution is shown to be second order convergent in the discrete L ∞ − norm. A numerical example shows the efficiency of the proposed scheme. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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