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^ = ^ 1 " (1) It bx * ; where x, t are the distance and time co-ordinates respectively. Most of these, together with conditions for their stability, can be found in works such as Richtmyer (1957), Forsythe and Wasow (1960), Collatz (1960), and Saul'ev (1962). In the main, the formulae in common use tend to be simple formulae with stability conditions which permit relatively large time steps. There are, however, many problems involving equations of the heat conduction type where very high accuracy is required over a small range of the time co-ordinate. Thus formulae of high accuracy are required which need only be stable for small values of the mesh ratio. In view of the high-speed computing facilities now available these formulae can also, of course, be used to give high accuracy results over any range of the time co-ordinate.

High Accuracy Difference Formulae for the Numerical Solution of the Heat Conduction Equation