SIAM Journal on Numerical Analysis · 1984 · 62 citations · 10 references
Natural SciencesMathematicsComputational MechanicsDifferential EquationsFluid DynamicsConvergence AnalysisNumerical AlgorithmsNumerical AnalysisNumerical ConvergenceNumerical Methods For Differential EquationsNumerical StabilityAsymptotic TheoryConvergenceNumerical Solutions Of Ordinary Differential EquationsOrdinary Differential Equation SolversStability Of Numerical Schemes
In this paper variable-stepsize, variable-formula, multistep methods for the numerical solution of ordinary differential equations are considered. Some more general results on stability than are given in the papers of Gear–Tu [SIAM J. Numer. Anal., 11 (1974), pp. 1025–1043] and Gear–Watanabe [SIAM J. Numer. Anal., 11 (1974), pp. 1044–1058] are obtained. Further, the asymptotic behavior of the error in the variable-stepsize, fixed-formula case is studied. Finally, the above study is extended to predictor-corrector methods.
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