Semilinear parabolic problems with nonlocal Dirichlet boundary conditions

Abstract

A semilinear parabolic problem with a nonlocal Dirichlet boundary condition is studied. This article presents a new and very easy implementable numerical algorithm for computations. This is based on a suitable linearization in time. The derived algorithm is implicit and it does not need any iteration process to get a solution with the nonlocal boundary condition. The stability analysis has been performed and the convergence of approximations towards a solution of the continuous problem is shown. The uniqueness of a solution is proved. Error estimates for the time discretization are derived.