ABSTRACT
For any numerical technique it is essential to consider the sources of error and how they are propagated through a calculation. This is particularly important for the solution of differential equations which demands a step-by-step approach. The development of numerical methods often is concerned more directly with A rather than with B, since the arithmetic precision, or the number of significant digits carried through an arithmetic operation, of a computer is usually beyond the control of the mathematician. Since the rounding error in any lengthy calculation will depend directly on the number of arithmetic operations carried out, it may be reduced by minimising this number. A successful numerical method for differential equations should permit the computation of solutions, from the mathematical point of view, to any desired accuracy. In practice, the accuracy will be subject to the limitations of machine precision.
