Mean Square Consistency On Numerical Solutions of Stochastic Wave Equation with Cubic Nonlinearities on 2D Rectangles

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...

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Main Author: Hazaimeh Haziem M.
Format: Article
Language:English
Published: EDP Sciences 2017-01-01
Series:MATEC Web of Conferences
Online Access:https://doi.org/10.1051/matecconf/201712505020
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spelling doaj-6ec25fb2e5ef45e1a48ab4641437a3782021-02-02T03:51:26ZengEDP SciencesMATEC Web of Conferences2261-236X2017-01-011250502010.1051/matecconf/201712505020matecconf_cscc2017_05020Mean Square Consistency On Numerical Solutions of Stochastic Wave Equation with Cubic Nonlinearities on 2D RectanglesHazaimeh Haziem M.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.https://doi.org/10.1051/matecconf/201712505020
collection DOAJ
language English
format Article
sources DOAJ
author Hazaimeh Haziem M.
spellingShingle Hazaimeh Haziem M.
Mean Square Consistency On Numerical Solutions of Stochastic Wave Equation with Cubic Nonlinearities on 2D Rectangles
MATEC Web of Conferences
author_facet Hazaimeh Haziem M.
author_sort Hazaimeh Haziem M.
title Mean Square Consistency On Numerical Solutions of Stochastic Wave Equation with Cubic Nonlinearities on 2D Rectangles
title_short Mean Square Consistency On Numerical Solutions of Stochastic Wave Equation with Cubic Nonlinearities on 2D Rectangles
title_full Mean Square Consistency On Numerical Solutions of Stochastic Wave Equation with Cubic Nonlinearities on 2D Rectangles
title_fullStr Mean Square Consistency On Numerical Solutions of Stochastic Wave Equation with Cubic Nonlinearities on 2D Rectangles
title_full_unstemmed Mean Square Consistency On Numerical Solutions of Stochastic Wave Equation with Cubic Nonlinearities on 2D Rectangles
title_sort mean square consistency on numerical solutions of stochastic wave equation with cubic nonlinearities on 2d rectangles
publisher EDP Sciences
series MATEC Web of Conferences
issn 2261-236X
publishDate 2017-01-01
description 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.
url https://doi.org/10.1051/matecconf/201712505020
work_keys_str_mv AT hazaimehhaziemm meansquareconsistencyonnumericalsolutionsofstochasticwaveequationwithcubicnonlinearitieson2drectangles
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