Abstract

A major motivation for studying discrete equations is the continuing advancements in computational techniques and their applications to solving differential equations by approximative difference equations.

The existence of a solution to a differential equation does not necessarily imply the existence of a solution to its discretization.

Thus the need to develop theory which guarantees the existence of solutions to continuous problems and their discretization, is naturally raised.

This work provides results for a priori bounds, existence and convergence of solutions for discretized boundary value problems in a variety of settings.