Parallel monotone iterative relaxation methods for a class of two-dimensional discrete boundary value problems (Q1827151)

Two-dimensional discrete boundary value problems are considered. A parallel monotone iterative relaxation method for a class of problems is established, and the sequence of iterations is shown to converge monotonically either from above or below to a solution of the problem. Existence and comparison results of upper and lower solutions are given and a parallel computational algorithm is constructed. The local and global existence and uniqueness of the solution are obtained. The rate convergence of the iterations is analyzed.