A Method for Discretization in Time Based on Cayley Transform for Parabolic Transmission Problem

摘要

A new numerical technique for time discretization is applied for numerical solving of transmission problem for an one-dimensional heat conduction equation. The method is based on Cayley transform and has accuracy like spectral methods. In order to emphasize on features of the numerical approach, we use finite difference method as a simplest one for space discretization. Convergence results are presented. It is shown that the convergence rate of fully discrete solution to exact one is determined by accuracy of method for space discretization.