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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