Numerical Methods for Ordinary Differential Equations: Butcher/Numerical Methods

Keywords

Ordinary differential equation, Mathematics, Applied mathematics, Computer science, Mathematical analysis

References

• Classical Fifth-, Sixth-, Seventh-, and Eighth-Order Runge-Kutta Formulas with Stepsize ControlE. Fehlberg — 1968
• Generalized disks of contractivity for explicit and implicit Runge-Kutta methodsGermund Dahlquist, Rolf Jeltsch — 1979
• Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential EquationsErnst Hairer, Christian Lubich, Gerhard Wanner — 2004
• General Linear Methods for Stiff Differential EquationsJ. C. Butcher — 2001
• On the Butcher group and general multi-value methodsE. Hairer, Gerhard Wanner — 1974
• Some properties of symplectic Runge-Kutta methodsErnst Hairer, Pierre Leone — 2000
• Explicit General Linear Methods with Inherent Runge–Kutta StabilityWilliam M. D. Wright — 2002
• Automatic Control and Adaptive Time-SteppingGustaf Söderlind — 2002
• Parallel Diagonally Implicit Multistage Integration Methods for Stiff Ordinary Differential EquationsAnjana Devi Singh — 1999
• A special stability problem for linear multistep methodsGermund Dahlquist — 1963
• A stability property of implicit Runge-Kutta methodsJ. C. Butcher — 1975
• Some Explicit Runge”Kutta Methods of High OrderGregory S. Cooper, J. H. Verner — 1972
• One-Leg Formulas for Stiff Ordinary Differential EquationsDaniel S. Watanabe, Qasim Mohammad Sheikh — 1984
• A special family of Runge-Kutta methods for solving stiff differential equationsKevin Burrage — 1978
• Cyclic composite multistep predictor-corrector methodsEldon Hansen — 1969
• An introduction to “almost Runge-Kutta” methodsJ. C. Butcher — 1997
• Quasi double-precision in floating point additionOle Møller — 1965
• Construction of high order diagonally implicit multistage integration methods for ordinary differential equationsJ. C. Butcher, Z. Jackiewicz — 1998
• A Program for the Automatic Integration of Differential Equations using the Method of Taylor SeriesA. H. Gibbons — 1960
• Stability of Runge-Kutta Methods for Trajectory ProblemsGregory S. Cooper — 1987

Cited by

• Efficient calibration of a new Hobson-Rogers modelJ. Duijndam — 2013
• Summation-By-Parts Operators for Time Discretisation : Initial InvestigationsJan Nordström, Tomas Lundquist — 2012
• Bidirectional Control of Absence Seizures by the Basal Ganglia: A Computational EvidenceDaniel John Kubis — 2014
• Nanopositioning in Atomic Force Microscopes: Robust Control Design, Order Reduction and Numerical ImplementabilityMichael R. P. Ragazzon — 2013
• STABILITY AND CONVERGENCE FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONSOday Mohammed Waheeb — 2012
• Identification des coefficients aérodynamiques d'un projectile à partir de mesures prises en volHélène Demailly — 2011
• Comparison of Nonlinear Filtering Methods for Battery State of Charge EstimationKlaus Zhang — 2014
• To what extent do long-duration high-volume dam releases influence river–aquifer interactions? A case study in New South Wales, AustraliaPeter W. Graham, Martin S. Andersen, Matthew F. McCabe — 2015
• Numerical analysis of some integral equations with singularitiesSophy M. Thomas — 2006
• A new diagonally implicit Runge-Kutta-Nyström method for periodic IVPsNorazak Senu, Mohamed Suleiman, Fudziah Ismail — 2010
• Using analysis state to construct a forecast error covariance matrix in ensemble Kalman filter assimilationXiaogu Zheng, Guocan Wu, Shupeng Zhang — 2013
• From resurgent functions to real resummation through combinatorial Hopf algebrasEmmanuel Vieillard-Baron — 2014
• Convergence of an implicit runge-kutta discontinuous Galerkin method using smooth limitersJacob Middag — 2012
• Probabilistic solution of differential equations for Bayesian uncertainty quantification and inferenceOksana Chkrebtii — 2013
• A fourth-order diagonally implicit Runge-Kutta-Nyström method with dispersion of high orderNorazak Senu, Mohamed Suleiman, Fudziah Ismail — 2010
• THE LIE-INTEGRATOR AND THE HÉNON-HEILES SYSTEMIharka Szücs-Csillik — 2010
• On the dynamics of human locomotion and co-design of lower limb assistive devicesJ. V. D. Kieboom — 2014
• A Hybrid Spectral-Element / Finite-Element Time-Domain Method for Multiscale Electromagnetic SimulationsJiefu Chen — 2010
• On the use of the uniform complex scaling-method for studying time-dependent systemsJ. Bengtsson — 2012
• Solid-boundary treatment for moment systemsLoc H. Khieu — 2012

Related papers

• DETERMINING QUALITY REQUIREMENTS AT THE UNIVERSITIES TO IMPROVE THE QUALITY OF EDUCATIONNor Hanim Mustafa, Dinmukhamed Kelesbayev, Zh.D. Alibekova — 2018
• Primärzerlegung in Steinschen AlgebrenOtto Förster — 1964
• Über unirationale Scharen auf algebraischen MannigfaltigkeitenLudwig Reich — 1966
• Algebraic Set Operations, Multifunctions, and Indefinite IntegralsMilan V. Jovanović, Veselin Jungić — 1996
• On Almost α(Λ, sp)-continuous MultifunctionsChawalit Boonpok, Jeeranunt Khampakdee — 2022
• Produkttreue Klassen universeller AlgebrenJürgen Timm — 1969
• Approximation of fixed points of multifunctions in partial metric spacesDaniela Paesano — 2015
• The World of Jagdish N. SrivastavaSubir Ghosh, Sudhir Gupta, Rahul Mukerjee — 2013
• Direct estimation of SIR model parameters through second‐order finite differencesMarina Medvedeva, Theodore E. Simos, Ch. Tsitouras — 2020