# American Institute of Mathematical Sciences

## Numerical solution of partial differential equations with stochastic Neumann boundary conditions

 Department of Mathematics, Faculty of Sciences, Razi University, Kermanshah, Iran

Received  May 2018 Revised  November 2018 Published  April 2019

The aim of this paper is to study the numerical solution of partial differential equations with boundary forcing. For spatial discretization we apply the Galerkin method and for time discretization we will use a method based on the accelerated exponential Euler method. Our purpose is to investigate the convergence of the proposed method, but the main difficulty in carrying out this construction is that at the forced boundary the solution is expected to be unbounded. Therefore the error estimates are performed in the $L_p$ spaces.

Citation: Minoo Kamrani. Numerical solution of partial differential equations with stochastic Neumann boundary conditions. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2019061
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##### References:
Numerical solution of Example 1, for $N = 32$, $\epsilon = 0.01$ and $T = \frac{3}{20}$, $\Delta t = 10^{-4}$
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