Mathematics of Computation · 1986 · 183 citations · 15 references
Natural SciencesComputational EngineeringMathematicsComputational MechanicsDifferential EquationsDiscrete MathematicsApproximation MethodsConvergence AnalysisNumerical AlgorithmsNumerical AnalysisNumerical ConvergenceNumerical Methods For Differential EquationsDifferential Equation SolversDiscrete Approximation SchemesTime DiscretizationTime-stepping Schemes
The present paper develops a theory of Natural Continuous Extensions (NCEs) for the discrete approximate solution of an ODE given by a Runge-Kutta process. These NCEs are defined in such a way that the continuous solutions furnished by the one-step collocation methods are included.
15