Implicit Runge-Kutta formulae with built-in estimates of the accumulated truncation error

DOI10.1007/BF02239977zbMath0627.65083MaRDI QIDQ1092624

Walter R. Richert

Publication date: 1987

Published in: Computing (Search for Journal in Brave)

zbMATH Keywords

error estimates\(A\)-stabilityimplicit Runge-Kutta methodstrue error\(A\)-stable methodsaccumulated truncation error

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

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Generalizing global error estimation for ordinary differential equations by using coupled time-stepping methods

Cites Work

• Some old and new Runge-Kutta formulas with stepsize control and their error coefficients
• Runge-Kutta integration algorithms with built-in estimates of the accumulated truncation error
• Numerical solution of ordinary differential equations
• Global Error Estimation with Runge--Kutta Methods
• An Algorithm for Least-Squares Estimation of Nonlinear Parameters
• Comparing numerical methods for stiff systems of O.D.E:s
• Global Error Estimates for Ordinary Differential Equations
• Coefficients for the study of Runge-Kutta integration processes
• Local Estimation of the Global Discretization Error
• A-stable Runge-Kutta processes
• A method for the solution of certain non-linear problems in least squares
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