Stability of theta-schemes in the numerical solution of a partial differential equation with piecewise continuous arguments

摘要

A finite difference method, namely the theta-scherne, is used to solve a partial differential equation with piecewise continuous arguments. First, an example is given to show that the results for original PDEs do not hold for PDEs with piecewise continuous arguments. Next, for the mesh ratio satisfying certain conditions, the stability of this scheme is obtained.