Implicit Euler method for numerical solution of nonlinear stochastic partial differential equations with multiplicative trace class noise

被引：6

作者：

Kamrani, Minoo ^{[1
]}

Hosseini, S. Mohammad ^{[2
]}

Hausenblas, Erika ^{[3
]}

机构：

[1] Razi Univ, Dept Math, Fac Sci, Kermanshah, Iran

[2] Tarbiat Modares Univ, Dept Appl Math, Tehran, Iran

[3] Univ Leoben, Dept Math & Informat Technol, Leoben, Austria

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2018年 / 41卷 / 13期

基金：

奥地利科学基金会;

关键词：

L-2; convergence; semi-implicit Euler method; spectral collocation method; stochastic partial differential equation; FINITE-ELEMENT METHODS; EVOLUTION EQUATIONS; BURGERS-EQUATION; ADDITIVE NOISE; APPROXIMATION; DRIVEN; DISCRETIZATION; REGULARITY; PDES;

D O I：

10.1002/mma.4946

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the numerical approximation of stochastic partial differential equations with nonlinear multiplicative trace class noise. Discretization is obtained by spectral collocation method in space, and semi-implicit Euler method is used for the temporal approximation. Our purpose is to investigate the convergence of the proposed method. The rate of convergence is obtained, and some numerical examples are included to illustrate the estimated convergence rate.

引用

页码：4986 / 5002

页数：17

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