In this thesis, general conditions on the coefficients of difference equations are obtained which insure the convergenceof solutions of these difference equations to the solutions ofthe corresponding partial differential equations. A generalmethod which is applicable to a wide variety of partial differentialequations is presented here. However, in order to simplifythe presentation of this method and to leave out calculations which are not essential to the description of the method,the discussion is centered about the partial differential equations
əu/əy = c əu/əx and ə2u/əx2 = ə2u/əy2.
The treatment of these simpler problems then serves to indicatethe method for more general problems.
