SIAM Journal on Numerical Analysis · 1973 · 78 citations · 9 references
Numerical AnalysisEngineeringAnalysis Of AlgorithmComputational ComplexityEmpirical AlgorithmicsComputational MechanicsNumerical ComputationAlgorithm DesignMultistep MethodsNumerical SimulationSystems EngineeringNumerical StabilityParallel ComputingCombinatorial OptimizationApproximation TheoryDifference FormulationsHalving ProcessStep SizeComputer EngineeringComputer ScienceNumerical Method For Partial Differential EquationFinite Element MethodComputational ScienceNumerical TreatmentMultiscale Modeling
Approximately ten different ways for changing the step size used by multistep methods are enumerated, and their good and bad features are compared. More efficient algorithms are given for the difference formulations of a frequently used halving and doubling process, and a cure for the instability inherent in this halving process is proposed.
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The numerical integration of ordinary differential equations
C. W. Gear · Mathematics of Computation · 1967 · 185 citations