Adaptive stiff solvers at low accuracy and complexity

DOI10.1016/j.cam.2005.06.041zbMath1089.65061OpenAlexW1997904160MaRDI QIDQ2488889

Riccardo Fazio, Alessandra Jannelli

Publication date: 16 May 2006

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2005.06.041

zbMATH Keywords

performancealgorithmstabilitynumerical exampleserror estimationstiff systemsRosenbrock methodsbackward differentiation formula methodlow complexityAdaptive step sizeLinearly implicit and implicit methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70) Complexity and performance of numerical algorithms (65Y20) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (4)

Extended scaling invariance of one-dimensional models of liquid dynamics in a horizontal capillary ⋮ Well-posed initial conditions and numerical methods for one-dimensional models of liquid dynamics in a horizontal capillary ⋮ Comparison of some recent numerical methods for initial-value problems for stiff ordinary differential equations ⋮ Integration of chemical stiff ODEs using exponential propagation method

Uses Software

• Matlab
• CLAWPACK
• ode23
• ode45
• Ode15s
• ode113
• ode23s
• MATLAB ODE suite

Cites Work

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• A family of embedded Runge-Kutta formulae
• Singular perturbation methods for ordinary differential equations
• Moving-mesh methods for one-dimensional hyperbolic problems using CLAWPACK.
• Numerical time integration for air pollution models
• Continuous numerical methods for ODEs with defect control
• A 3D mathematical model for the prediction of mucilage dynamics
• A simple step size selection algorithm for ODE codes
• Numerical treatment of ordinary differential equations by extrapolation methods
• Klassische Runge-Kutta-Formeln fünfter und siebenter Ordnung mit Schrittweiten-Kontrolle
• The MATLAB ODE Suite
• Analysis of Error Control Strategies for Continuous Runge–Kutta Methods
• Explicit Runge–Kutta Methods with Estimates of the Local Truncation Error
• A Second-Order Rosenbrock Method Applied to Photochemical Dispersion Problems
• On the Construction and Comparison of Difference Schemes
• Integration of Stiff Equations

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