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Predictor-corrector procedures for systems of ordinary differential equations Zahar, Ramsay Vincent Michel

Abstract

Some of the most accurate and economical of the known numerical methods for solving the initial-value problem [Formula omitted] are of the predictor-corrector type. For systems of equations, the predictor-corrector procedures are defined in the same manner as they are for single equations. For a given problem and domain of t , a plot of the maximum error in the numerical approximation to x(t) obtained by a predictor-corrector procedure, versus the step-size, can be divided into three general regions - round-off, truncation, and instability. The most practical procedures are stable and have a small truncation error. The stability of a method depends on the magnitudes of the eigenvalues of a certain matrix that is associated with the matrix [Formula omitted] When the functions f[subscript i] are complicated, predictor-corrector procedures involving two evaluations per step seem to be the most efficient for general-purpose applications.

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