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

共 50 条

[21] A variational approach to nonlinear stochastic differential equations with linear multiplicative noise
Barbu, Viorel
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2019, 25
[22] On the stochastic Euler-Poincaré equations driven by pseudo-differential/multiplicative noise
Tang, Hao
JOURNAL OF FUNCTIONAL ANALYSIS, 2023, 285 (09)
[23] Euler Wavelet Method as a Numerical Approach for the Solution of Nonlinear Systems of Fractional Differential Equations
Polat, Sadiye Nergis Tural
Dincel, Arzu Turan
FRACTAL AND FRACTIONAL, 2023, 7 (03)
[24] A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise
Wang, Xiaojie
Gan, Siqing
Wang, Desheng
BIT NUMERICAL MATHEMATICS, 2012, 52 (03) : 741 - 772
[25] A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise
Xiaojie Wang
Siqing Gan
Desheng Wang
BIT Numerical Mathematics, 2012, 52 : 741 - 772
[26] Strong approximation of monotone stochastic partial differential equations driven by multiplicative noise
Zhihui Liu
Zhonghua Qiao
Stochastics and Partial Differential Equations: Analysis and Computations, 2021, 9 : 559 - 602
[27] An operatorial approach to stochastic partial differential equations driven by linear multiplicative noise
Barbu, Viorel
Roeckner, Michael
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2015, 17 (07) : 1789 - 1815
[28] A splitting algorithm for stochastic partial differential equations driven by linear multiplicative noise
Barbu, Viorel
Roeckner, Michael
STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, 2017, 5 (04): : 457 - 471
[29] On smooth approximation for random attractor of stochastic partial differential equations with multiplicative noise
Fu, Hongbo
Liu, Xianming
Liu, Jicheng
Wang, Xiangjun
STOCHASTICS AND DYNAMICS, 2018, 18 (05)
[30] A splitting algorithm for stochastic partial differential equations driven by linear multiplicative noise
Viorel Barbu
Michael Röckner
Stochastics and Partial Differential Equations: Analysis and Computations, 2017, 5 : 457 - 471

← 1 2 3 4 5 →