A fully discrete approximation of the one-dimensional stochastic wave equation

被引：32

作者：

Cohen, David ^{[1
]}

Quer-Sardanyons, Lluis ^{[2
]}

机构：

[1] Umea Univ, Matemat & Matemat Stat, S-90187 Umea, Sweden

[2] Univ Autonoma Barcelona, Dept Matemat, Bellaterra 08193, Spain

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2016年 / 36卷 / 01期

基金：

瑞典研究理事会;

关键词：

nonlinear stochastic wave equation; multiplicative noise; strong convergence; finite differences; stochastic trigonometric methods; PARTIAL-DIFFERENTIAL-EQUATIONS; FINITE-ELEMENT METHODS; NUMERICAL APPROXIMATION; LATTICE APPROXIMATIONS; TIME; DISCRETIZATION; DRIVEN; SCHEME;

D O I：

10.1093/imanum/drv006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A fully discrete approximation of one-dimensional nonlinear stochastic wave equations driven by multiplicative noise is presented. A standard finite difference approximation is used in space and a stochastic trigonometric method is used for the temporal approximation. This explicit time integrator allows for error bounds in LP(Omega), uniformly in time and space, in such a way that the time discretization does not suffer from any kind of CFL-type step-size restriction. Moreover, uniform almost sure convergence of the numerical solution is also proved. Numerical experiments are presented and confirm the theoretical results.

引用

页码：400 / 420

页数：21

共 50 条

[21] On the spectrum of discrete Schrodinger equation with one-dimensional perturbation
Borzov, V. V.
Damaskinsky, E. V.
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON DAYS ON DIFFRACTION 2016 (DD), 2016, : 73 - 78
[22] One-dimensional stochastic heat equation with discontinuous conductance
Zili, Mounir
Zougar, Eya
APPLICABLE ANALYSIS, 2019, 98 (12) : 2178 - 2191
[23] STABILITY AND ACCURACY ANALYSIS OF SOME FULLY-DISCRETE ALGORITHMS FOR THE ONE-DIMENSIONAL 2ND-ORDER WAVE-EQUATION
HUGHES, TJR
TEZDUYAR, TE
COMPUTERS & STRUCTURES, 1984, 19 (04) : 665 - 668
[24] Comparison of stochastic and approximation algorithms for one-dimensional cutting problems
Bingul, Z
Oysu, C
ADVANCES IN INTELLIGENT COMPUTING, PT 1, PROCEEDINGS, 2005, 3644 : 976 - 985
[25] One-dimensional approximation to stochastic lattice system with strong coupling
Lv, Wei
Lv, Yan
PHYSICS LETTERS A, 2009, 373 (31) : 2722 - 2728
[26] ON NUMERICAL MODELING OF ONE-DIMENSIONAL STOCHASTIC WAVE PROBLEMS
YAROSHCHUK, IO
USSR COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1984, 24 (06): : 97 - 99
[27] One-Dimensional Nonequilibrium Radiation-Transport Equation under Diffusion Approximation and Its Discrete Scheme
Gao, Qi
Zhang, Chuanfei
Zhou, Lin
Li, Zhenghong
Wu, Zeqing
Lei, Yu
Zhang, Chunlai
Zu, Xiaotao
ADVANCES IN CONDENSED MATTER PHYSICS, 2014, 2014
[28] An approximation result and Monte Carlo simulation of the adapted solution of the one-dimensional backward stochastic differential equation
Sghir, A.
Seghir, D.
Hadiri, S.
RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2018, 26 (03) : 131 - 142
[29] STABLE EXPLICIT DIFFERENCE APPROXIMATION OF ONE-DIMENSIONAL DIFFUSION EQUATION
JOUBERT, GR
COMPUTING, 1973, 11 (04) : 315 - 325
[30] Example of resonance scattering for the one-dimensional wave equation
Arsen'ev, AA
SBORNIK MATHEMATICS, 1999, 190 (5-6) : 783 - 790

← 1 2 3 4 5 →