A new eighth-order A-stable method for solving differential systems arising in chemical reac\-tions

DOI10.1007/s10910-006-9121-xzbMath1103.92057OpenAlexW1973941829MaRDI QIDQ862870

Jesus Vigo Aguiar, Higinio Ramos

Publication date: 24 January 2007

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-006-9121-x

zbMATH Keywords

A-stabilityimplicit Runge-Kutta methodstiff problemsChebyshev points

Mathematics Subject Classification ID

Classical flows, reactions, etc. in chemistry (92E20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (11)

On the relations between B\(_2\)VMs and Runge-Kutta collocation methods ⋮ A note on variable step-size formulation of a Simpson's-type second derivative block method for solving stiff systems ⋮ 3-point block backward differentiation formula with an off-step point for the solutions of stiff chemical reaction problems ⋮ A piecewise-linearized algorithm based on the Krylov subspace for solving stiff ODEs ⋮ A new modified embedded 5(4) pair of explicit Runge-Kutta methods for the numerical solution of the Schrödinger equation ⋮ Adaptive second derivative multistep methods for solving stiff chemical problems ⋮ The new class of multistep multiderivative hybrid methods for the numerical solution of chemical stiff systems of first order IVPs ⋮ A new one-step method with three intermediate points in a variable step-size mode for stiff differential systems ⋮ An error embedded method based on generalized Chebyshev polynomials ⋮ An efficient optimized adaptive step-size hybrid block method for integrating differential systems ⋮ An efficient optimized adaptive step-size hybrid block method for integrating \(w^{\prime \prime} = F (t, w, w^\prime)\) directly

Uses Software

• RADAU
• RODAS
• Test Set IVP

Cites Work

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• A second-order scheme for the ``Brusselator reaction-diffusion system
• Stiff differential equations solved by Radau methods
• On error estimation in general linear methods for stiff ODEs
• On the implementation of implicit Runge-Kutta methods
• Integration of Stiff Equations
• General linear methods

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