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Numerical solution of stochastic partial differential equations using a collocation method
Author(s) -
Kamrani Minoo
Publication year - 2016
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201400080
Subject(s) - mathematics , orthogonal collocation , collocation method , collocation (remote sensing) , stochastic partial differential equation , lipschitz continuity , spectral method , stochastic differential equation , partial differential equation , mathematical analysis , numerical partial differential equations , numerical analysis , differential equation , ordinary differential equation , computer science , machine learning
In this article we apply spectral collocation method to find a numerical solution of stochastic partial differential equations (SPDEs). Spectral collocation method is known to be impressively efficient for PDEs. We investigate this method for numerical solution of SPDEs and we obtain its rate of convergence. At first, the results are expressed for equations with globally Lipschitz coefficient, then we extend it to cases with locally Lipschitz coefficient. The analysis is supported by numerical results for some important SPDEs such as stochastic Kuramoto‐Sivashinksy equation.