Numerical Methods for Semilinear Elliptic Boundary Value Problems

摘要

In this paper, we present two kinds of numerical methods: the iterative method and the Riesz projection method for semilinear elliptic boundary value problems. A criterion for the convergence of the approximate solutions by each method is established. Numerical examples employing these two methods are given. We construct a coupling method combining the scaling iterative algorithm and the Riesz projection method. Using this method, we compute and visualize the positive solution of the semilinear elliptic boundary value problem. Several test problems are implemented.