ABSTRACT
Many physical processes important in science and engineering are modelled by partial differential equations. The numerical analysis of these is usually presented quite separately from that devoted to ordinary differential equations. Finite element techniques have dominated the research effort in problems involving several independent variables but finite difference methods are still popular in practical situations. The finite difference method has been covered extensively in a number of specialized texts and so do not propose to describe this conventional technique. Although implicit Runge-Kutta and multistep processes can be unconditionally stable, their computational cost per step is rather higher explicit methods. As in the numerical solution of ordinary differential equations the importance of variable step-sizes must be emphasised. With functions of two or more independent variables it is sometimes advantageous to vary the space mesh with time.
