Difference Methods and Soft Solutions

Abstract

This chapter discusses the generalized soft and weal solutions of certain classes of partial differential equations using difference methods. The soft solutions of differential equations lead in a natural way to difference methods. The chapter shows discusses how to obtain various difference methods from the soft solution. In difference methods for initial value problems, it frequently happens that the initial function is known only at a discrete set of points. Under such circumstances, it is still possible to verify functional relation by extending the definition of the initial data to all points on the initial line.