Some Theoretical and Computational Matters Relating to Predictor-corrector Methods of Numerical Integration

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Abstract
This paper is mainly concerned with three matters relating to predictor-corrector methods. The first is a consideration of the replacement of classical predictors by direct extrapolation, smoothed and unsmoothed, of the first derivative. The second matter discussed is the computational aspects of not iterating the corrector to convergence and the possible use of a convergence factor to test the corrector convergence. Finally, the desirability of using higher order processes as opposed to modifying the results of lower order processes is considered. Some numerical results are given to illustrate the topics discussed. This paper is based on one that was presented at the July 1960 Conference of the British Computer Society in Harrogate.

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