Mean Square Consistency On Numerical Solutions of Stochastic Wave Equation with Cubic Nonlinearities on 2D Rectangles
In this article we study the mean square consistency on numerical solutions of stochastic wave equations with cubic nonlinearities on two dimensional rectangles. In [8], we proved that the strong Fourier solution of these semi-linear wave equations exists and is unique on an appropriate Hilbert spac...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2017-01-01
|
| Series: | MATEC Web of Conferences |
| Online Access: | https://doi.org/10.1051/matecconf/201712505020 |
| Summary: | In this article we study the mean square consistency on numerical solutions of stochastic wave equations with cubic nonlinearities on two dimensional rectangles. In [8], we proved that the strong Fourier solution of these semi-linear wave equations exists and is unique on an appropriate Hilbert space. A linear-implicit Euler method is used to discretize the related Fourier coefficients. We prove that the linear-implicit Euler method applied to a solution of nonlinear stochastic wave equations in two dimensions is mean square consistency under the geometric condition. |
|---|---|
| ISSN: | 2261-236X |