Positive and conservative schemes for mass action kinetics

DOI10.1016/0898-1221(96)00142-3zbMath0859.92030OpenAlexW2084905094MaRDI QIDQ1816659

Enrico Bertolazzi

Publication date: 19 December 1996

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(96)00142-3

zbMATH Keywords

discretizationnonlinear systemsnonnegative solutionRunge-Kutta methodsEuler schemepositivity preservationimplicit schemesfirst-order schemeBrouwer fixed pointatomic mass conservationdiscretization of mass action kineticslinear first integralsrepeated inversion of \(M\)-matricessecond-order schemes

Mathematics Subject Classification ID

Classical flows, reactions, etc. in chemistry (92E20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Chemical kinetics in thermodynamics and heat transfer (80A30) Numerical methods for ordinary differential equations (65L99)

Related Items

A structure-preserving, operator splitting scheme for reaction-diffusion equations with detailed balance ⋮ Positivity-preserving methods for ordinary differential equations ⋮ A Second-Order Accurate, Operator Splitting Scheme for Reaction-Diffusion Systems in an Energetic Variational Formulation ⋮ An asymptotic preserving scheme for the streamer simulation ⋮ On the dynamics of first and second order GeCo and gBBKS schemes ⋮ A comprehensive theory on generalized BBKS schemes ⋮ An efficient algorithm for corona simulation with complex chemical models ⋮ Quadratic first integrals of kinetic differential equations ⋮ Extension of modified Patankar-Runge-Kutta schemes to nonautonomous production-destruction systems based on Oliver's approach ⋮ Unconditionally strong stability preserving extensions of the TR-BDF2 method ⋮ A triangle-based unstructured finite volume method for chemically reactive hypersonic flows ⋮ A finite volume scheme for two‐dimensional chemically reactive hypersonic flow

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Modern convergence theory for stiff initial-value problems
• On smoothing and order reduction effects for implicit Runge-Kutta formulae
• Multistep high-order interpolants of Runge-Kutta methods
• Some schemes for the implementation of implicit Runge-Kutta methods
• The dichotomy of stiffness: Pragmatism versus theory
• Solving stiff system by Taylor series
• On the Algebraic Equations in Implicit Runge–Kutta Methods
• Efficiently Implementable Algebraically Stable Runge–Kutta Methods
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
• Contractivity of Waveform Relaxation Runge–Kutta Iterations and Related Limit Methods for Dissipative Systems in the Maximum Norm
• Complete Algebraic Characterization of A-Stable Runge–Kutta Methods
• Stability of Runge–Kutta Methods for Stiff Ordinary Differential Equations
• A New Theoretical Approach to Runge–Kutta Methods