Local error control in codes for ordinary differential equations

L. F. Shampine

Type: Article

Publication Date: 1977-01-01

Citations: 32

DOI: https://doi.org/10.1016/0096-3003(77)90001-7

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Applied Mathematics and Computation - View

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Works That Cite This (29)

Action	Title	Year	Authors
+	A simple local error estimator and an adaptive time‐stepping procedure for direct integration method in dynamic analysis	1993	Xiaodong Li Ling Fu Zeng N.‐E. Wiberg
+	Blockwise Adaptivity for Time Dependent Problems Based on Coarse Scale Adjoint Solutions	2010	Varis Carey Donald Estep August Johansson Mats G. Larson Simon Tavener
+	Global error estimation with runge-kutta triples	1989	John R. Dormand Mike Lockyer N.E. McGorrigan P.J. Prince
+	Adaptive time stepping for fluid-structure interaction solvers	2017	Matthias Mayr Wolfgang A. Wall Michael W. Gee
+	Global error estimation based on the tolerance proportionality for some adaptive Runge–Kutta codes	2007	M. Calvo S. González‐Pinto J.I. Montijano
+	Kateatutako Runge-Kutta metodoek eskaintzen duten koste baxuko errorea	2013	Elisabete Alberdi
+	A post‐processing technique and an <i>a posteriori</i> error estimate for the newmark method in dynamic analysis	1993	N.‐E. Wiberg Xiaodong Li
+	Global Error versus Tolerance for Explicit Runge-Kutta Methods	1991	Desmond J. Higham
+	Time Integration Schemes in Dynamic Problems- Effect of Damping on Numerical Stability and Accuracy	2016	Ashish Aeran Hirpa G. Lemu
+	Interpolation for Runge–Kutta Methods	1985	L. F. Shampine

Works Cited by This (8)

Action	Title	Year	Authors
+	Changing stepsize in the integration of differential equations using modified divided differences	1974	Fred T. Krogh
+	Comparing Numerical Methods for Ordinary Differential Equations	1972	T. E. Hull W. H. Enright B. M. Fellen A. E. Sedgwick
+ PDF Chat	On Testing a Subroutine for the Numerical Integration of Ordinary Differential Equations	1973	Fred T. Krogh
+	Test Results on Initial Value Methods for Non-Stiff Ordinary Differential Equations	1976	W. H. Enright T. E. Hull
+	Automatic numerical integration	1964	Jaap Zonneveld
+ PDF Chat	Local extrapolation in the solution of ordinary differential equations	1973	L. F. Shampine
+	Solving Nonstiff Ordinary Differential Equations—The State of the Art	1976	L. F. Shampine H.A. Watts S.M. Davenport
+	DESUB: INTEGRATION OF A FIRST-ORDER SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS	1971	Phyllis A. Fox