Single Step Fully Discrete Schemes for the Inhomogeneous Equation

Abstract

In this chapter we shall continue our study of single step fully discrete methods and turn now to such schemes for the inhomogeneous heat equation. Following the approach of Chapter 7 we shall first consider discretization in time of an ordinary differential equation in a Hilbert space setting, and then apply our results to the spatially discrete equation. In view of the work in Chapter 7 for the homogeneous equation with given initial data, we restrict ourselves here to the case that the initial data vanish.