An Iterative Process for the Solution of Semi-Linear Elliptic Equations with Discontinuous Coefficients and Solution

摘要

We consider and investigate boundary value problems (BVPs) for semi-linear elliptic equations with discontinuous coefficients and solutions (with imperfect contact matching conditions). Finite difference approximations of these problems are constructed. An iterative method for solving difference BVPs of contact for semi-linear elliptic equations with iterations on the inner boundary where the coefficients and solutions are discontinuous is constructed and validated. The convergence rate of iterations (with calculated constants) is estimated.