Abstract
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 \begin{document}$ L_p $\end{document} spaces.
Highlights
This work was intended as an attempt to motivate numerical solution of partial differential equations with stochastic Neumann boundary conditions
In some applications such as chemical reactor theory [14], colloid and interface chemistry [21] the noise has an impact on the bulk and on the boundary. This leads to quite different interesting dynamical effects that are not yet studied with rigorous analytic methods
In recent years many papers addressed the questions of PDEs with boundary forcing
Summary
This work was intended as an attempt to motivate numerical solution of partial differential equations with stochastic Neumann boundary conditions. Many phenomena in science and engineering that may have been modeled by deterministic partial differential equations have some uncertainty, due to existence of different stochastic perturbations In some applications such as chemical reactor theory [14], colloid and interface chemistry [21] the noise has an impact on the bulk and on the boundary. In [4], Brzeniak, Goldys, Peszat, and Russo provided the analysis of elliptic and parabolic boundary value problems on bounded and unbounded domains with smooth boundary and with random Dirichlet boundary conditions This is significantly different from the case of noise in Neumann boundary conditions that we will. Where H2(G) is the standard-Sobolev space such that derivatives up to order 2 are in L2(G) and ∂νu|∂G is the normal derivative of u on ∂G
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
