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Implicit Euler method for numerical solution of nonlinear stochastic partial differential equations with multiplicative trace class noise
Author(s) -
Kamrani Minoo,
Hosseini S. Mohammad,
Hausenblas Erika
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4946
Subject(s) - mathematics , trace class , stochastic partial differential equation , backward euler method , discretization , rate of convergence , numerical partial differential equations , nonlinear system , partial differential equation , exponential integrator , collocation (remote sensing) , euler method , mathematical analysis , stochastic differential equation , multiplicative noise , convergence (economics) , euler's formula , collocation method , trace (psycholinguistics) , differential equation , ordinary differential equation , differential algebraic equation , hilbert space , philosophy , signal transfer function , analog signal , linguistics , quantum mechanics , physics , channel (broadcasting) , remote sensing , economic growth , engineering , digital signal processing , electrical engineering , economics , geology
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.