Six invited papers on computational methods of solving partial differential equations were presented at the 1981 Conference on Numerical Solutions of Partial Differential Equations held at the University of Melbourne, Australia. They were also printed as part of the Conference Proceedings titled Numerical Solutions of Partial Differential Equations, edited by J. Noye and published by the North-Holland Publishing Company. The articles were so well received that it was decided to expand them and print them in a separate book so that the material they contained would be more readily available to postgraduate students and research workers in Universities and Institutes of Technology and to scientists and engineers in other establishments.