Mildly nonlinear elliptic partial differential equations and their numerical solutoin. II

Abstract

Abstract : High speed digital computer methods are studied for obtaining solutions of difference equation analogues of mildly nonlinear elliptic boundary value problems. The problem is formulated in terms of finding a vector X which satisfies AX = - f(X) + Y, where A is an irreducible M matrix, Y is a given vector, and f is a given function. Two general iteration techniques and related convergence theorems are explored. The methods and ideas also extend to a large class of ordinary differential equation boundary value problems. (Author)