Numerical methods for scientists and engineers (2nd ed.)
Numerical methods for scientists and engineers (2nd ed.)
Stability of a Numerical Solution of Differential Equations
Journal of the ACM (JACM)
Stability of a Numerical Solution of Differential Equations—Part II
Journal of the ACM (JACM)
Stability Properties of Predictor-Corrector Methods for Ordinary Differential Equations
Journal of the ACM (JACM)
Generalized Multistep Predictor-Corrector Methods
Journal of the ACM (JACM)
A Modified Multistep Method for the Numerical Integration of Ordinary Differential Equations
Journal of the ACM (JACM)
Multistep Methods With Modified Predictors and Correctors
Journal of the ACM (JACM)
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In a previous paper the authors suggested that the accurate correctors proposed by Gragg and Stetter for solving ordinary differential equations should be accompanied by similar predictors. In each method in that paper the corrector and one of the predictors use one “nonstop” point within the interval of integration. In the present paper a corrector is dealt with in which two “nonstep” points are used, and in which, to some degree, the authors have “balanced” the contributions of the errors in the predictors to the total local truncation error, a technique due to Butcher.