Abstract
Two-parameter families of predictor-corrector methods based upon a combination of Adams- and Nyström formulae have been developed. The combinations use correctors of order one higher than that of the predictors. The methods are chosen to give optimal stability properties with respect to a requirement on the form and size of the regions of absolute stability. The optimal methods are listed and their regions of absolute stability are presented. The efficiency of the methods is compared to that of the corresponding Adams methods through numerical results from a variable order, variable stepsize program package.
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Thomsen, P.G., Zlatev, Z. Two-parameter families of predictor-corrector methods for the solution of ordinary differential equations. BIT 19, 503–517 (1979). https://doi.org/10.1007/BF01931267
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DOI: https://doi.org/10.1007/BF01931267