A variable-step variable-order algorithm for systems of stiff odes

DOI10.1080/00207169708804557zbMath0871.65076OpenAlexW2055500337MaRDI QIDQ3123359

T. Van Hecke, H. E. De Meyer, Marnix van Daele, Guido Vanden Berghe

Publication date: 7 October 1997

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207169708804557

zbMATH Keywords

stabilitynumerical resultsstiff systemsRunge-Kutta methodtest problemsone-step methodsvariable-step variable-order algorithm

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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Multiple scale methods for ordinary differential equations (34E13)

Related Items (4)

Numerical methods based on extended one-step methods for solving optimal control problems ⋮ Deferred correction with mono-implicit Runge-Kutta methods for first-order IVPs ⋮ Optimal extended one-step schemes of exponential type for stiff initial-value problems ⋮ A new variable step size block backward differentiation formula for solving stiff initial value problems

Uses Software

• NAG
• VODE
• RODAS
• nag

Cites Work

• Unnamed Item
• nag
• An \(A\)-stable extended trapezoidal rule for the integration of ordinary differential equations
• A family of embedded Runge-Kutta formulae
• A new approach to explain the 'high irradiance responses' of photomorphogenesis on the basis of phytochrome
• A class of stabilized extended one-step methods for the numerical solution of ODEs
• A general theory of stabilized extended one-step methods for odes
• Triangularly Implicit Iteration Methods for ODE-IVP Solvers
• Extended one-step methods for the numerical solution of ordinary differential equations
• Efficient higher order implicit one-step methods for integration of stiff differential equations
• Mono-implicit Runge—Kutta Formulae for the Numerical Integration of Stiff Differential Systems
• Gauss–Seidel Iteration for Stiff ODES from Chemical Kinetics

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