A Taylor expansion approach for solving partial differential equations with random Neumann boundary conditions |
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Authors: | Shengqiang Xu Jinqiao Duan |
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Affiliation: | Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA |
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Abstract: | Nonlinear partial differential equation with random Neumann boundary conditions are considered. A stochastic Taylor expansion method is derived to simulate these stochastic systems numerically. As examples, a nonlinear parabolic equation (the real Ginzburg-Landau equation) and a nonlinear hyperbolic equation (the sine-Gordon equation) with random Neumann boundary conditions are solved numerically using a stochastic Taylor expansion method. The impact of boundary noise on the system evolution is also discussed. |
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Keywords: | Random boundary conditions Real Ginzburg-Landau equation Sine-Gordon equation Stochastic Taylor expansion methods Impact of boundary noise |
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