On Stable Integration of Stiff Ordinary Differential Equations with Global Error Control

Lecture Notes in Computer Science - Computational Science – ICCS 2005 ◽

10.1007/11428831_6 ◽

2005 ◽

pp. 42-49

Author(s):

Gennady Yur’evich Kulikov ◽

Sergey Konstantinovich Shindin

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Error Control ◽

Global Error ◽

Stiff Ordinary Differential Equations ◽

Stable Integration

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A Singly Diagonally Implicit Two-Step Peer Triple with Global Error Control for Stiff Ordinary Differential Equations

SIAM Journal on Scientific Computing ◽

10.1137/140979952 ◽

2015 ◽

Vol 37 (3) ◽

pp. A1593-A1613 ◽

Cited By ~ 11

Author(s):

G. Yu. Kulikov ◽

R. Weiner

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Error Control ◽

Global Error ◽

Stiff Ordinary Differential Equations

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Global error control for the continuous Galerkin finite element method for ordinary differential equations

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/1994280708151 ◽

1994 ◽

Vol 28 (7) ◽

pp. 815-852 ◽

Cited By ~ 47

Author(s):

Donald Estep ◽

Donald French

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Error Control ◽

Global Error ◽

Galerkin Finite Element Method ◽

Galerkin Finite Element ◽

Continuous Galerkin ◽

Element Method

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INTEGRATOR: A Computational Tool to Solve Ordinary Differential Equations with Global Error Control

Computational Science - ICCS 2004 - Lecture Notes in Computer Science ◽

10.1007/978-3-540-24687-9_74 ◽

2004 ◽

pp. 570-573

Author(s):

Gennady Y. Kulikov ◽

Sergey K. Shindin

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Error Control ◽

Global Error ◽

Computational Tool

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Relative Global Error Control in the RKQ Algorithm for Systems of Ordinary Differential Equations

Journal of Mathematics Research ◽

10.5539/jmr.v3n4p59 ◽

2011 ◽

Vol 3 (4) ◽

Author(s):

Justin Steven Prentice

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Error Control ◽

Global Error

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A Posteriori Error Bounds and Global Error Control for Approximation of Ordinary Differential Equations

SIAM Journal on Numerical Analysis ◽

10.1137/0732001 ◽

1995 ◽

Vol 32 (1) ◽

pp. 1-48 ◽

Cited By ~ 126

Author(s):

Donald Estep

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Error Bounds ◽

Error Control ◽

Posteriori Error ◽

Global Error ◽

A Posteriori ◽

A Posteriori Error ◽

A Posteriori Error Bounds

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Nested Implicit Runge–Kutta Pairs of Gauss and Lobatto Types with Local and Global Error Controls for Stiff Ordinary Differential Equations

Computational Mathematics and Mathematical Physics ◽

10.1134/s0965542520070076 ◽

2020 ◽

Vol 60 (7) ◽

pp. 1134-1154

Author(s):

G. Yu. Kulikov

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Global Error ◽

Stiff Ordinary Differential Equations ◽

Runge Kutta

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New third- and fourth-order singly diagonally implicit two-step peer triples with local and global error controls for solving stiff ordinary differential equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2016.06.013 ◽

2017 ◽

Vol 316 ◽

pp. 380-391 ◽

Cited By ~ 7

Author(s):

R. Weiner ◽

G.Yu. Kulikov ◽

S. Beck ◽

J. Bruder

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Fourth Order ◽

Global Error ◽

Stiff Ordinary Differential Equations

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A Quasi-Steady-State Solver for the Stiff Ordinary Differential Equations of Reaction Kinetics

Journal of Computational Physics ◽

10.1006/jcph.2000.6605 ◽

2000 ◽

Vol 164 (2) ◽

pp. 407-428 ◽

Cited By ~ 62

Author(s):

David R. Mott ◽

Elaine S. Oran ◽

Bram van Leer

Keyword(s):

Steady State ◽

Differential Equations ◽

Reaction Kinetics ◽

Ordinary Differential Equations ◽

Quasi Steady State ◽

Stiff Ordinary Differential Equations

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Estimating the Global Error of Runge-Kutta Approximations for Ordinary Differential Equations

Differential-Difference Equations/Differential-Differenzengleichungen - International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique ◽

10.1007/978-3-0348-6767-2_6 ◽

1983 ◽

pp. 55-71 ◽

Cited By ~ 1

Author(s):

K. Dekker ◽

J. G. Verwer

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Global Error ◽

Runge Kutta

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Quantization-based new integration methods for stiff ordinary differential equations

SIMULATION ◽

10.1177/0037549711403645 ◽

2011 ◽

Vol 88 (4) ◽

pp. 387-407 ◽

Cited By ~ 11

Author(s):

Gustavo Migoni ◽

Ernesto Kofman ◽

François Cellier

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Integration Methods ◽

Stiff Ordinary Differential Equations

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