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2018•Mathematical Methods in the Applied SciencesRequires access

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

Minoo Kamrani, S. Mohammad Hosseini, Erika Hausenblas

Open publisher page 10 citations

Abstract

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.

About this research paper

What this paper is about

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.

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OpenAlex reports 10 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

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.

Key concepts: Mathematics, Trace class, Stochastic partial differential equation, Backward Euler method, Discretization, Rate of convergence, Numerical partial differential equations, Nonlinear system

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