Technique of the step-by-step integration of ordinary differential equations

In Part 1 step-by-step methods are examined critically and emphasis is placed on the dependence of the error on the number n of steps used for a given range of the independent variable. The index of a process is defined and it is shown that the errors can be assessed and partially corrected when the index is known and results obtained for two or more values of n. Attention is drawn to the advantages in certain cases of a part-analytical process. In Part 2 methods of numerical integration in general are classified and briefly reviewed. The chart, Table 2.2.1, summarises the classification.