Numerical solution of partial differential equations with stochastic Neumann boundary conditions. (English) Zbl 1420.65111
Summary: 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.
MSC:
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 37L65 | Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems |
