An improved and generalized second order, unconditionally positive, mass conserving integration scheme for biochemical systems

DOI10.1016/j.apnum.2006.12.002zbMath1136.65067OpenAlexW2085800969MaRDI QIDQ2479424

Yanyan Li

Publication date: 26 March 2008

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2006.12.002

zbMATH Keywords

algorithmmass conservationlinear systemsnonlinear systemsnumerical examplesRunge-Kutta methodsunconditional positivityPatankar-type-schemes

Mathematics Subject Classification ID

Classical flows, reactions, etc. in chemistry (92E20) Biochemistry, molecular biology (92C40) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Ordinary differential equations of infinite order (34A35)

Related Items (14)

Second-order unconditional positive preserving schemes for non-equilibrium reactive flows with mass and mole balance ⋮ Positivity-preserving methods for ordinary differential equations ⋮ On the Stability of Unconditionally Positive and Linear Invariants Preserving Time Integration Schemes ⋮ On order conditions for modified Patankar-Runge-Kutta schemes ⋮ A positive finite-difference model in the computational simulation of complex biological film models ⋮ On the stability of strong-stability-preserving modified Patankar–Runge–Kutta schemes ⋮ Some qualitative properties of the discrete models for malaria propagation ⋮ On the dynamics of first and second order GeCo and gBBKS schemes ⋮ A non-standard symmetry-preserving method to compute bounded solutions of a generalized Newell-Whitehead-Segel equation ⋮ A comprehensive theory on generalized BBKS schemes ⋮ A convergent and dynamically consistent finite-difference method to approximate the positive and bounded solutions of the classical Burgers-Fisher equation ⋮ \textit{GeCo}: geometric conservative nonstandard schemes for biochemical systems ⋮ Unconditionally positive and conservative third order modified Patankar-Runge-Kutta discretizations of production-destruction systems ⋮ Issues with positivity-preserving Patankar-type schemes

Cites Work

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• A second-order, unconditionally positive, mass-conserving integration scheme for biochemical systems
• A high-order conservative Patankar-type discretisation for stiff systems of production--destruction equations
• Positive numerical integration methods for chemical kinetic systems

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