Fully implicit time-stepping schemes and non-linear solvers for systems of reaction-diffusion equations

DOI10.1016/j.amc.2014.07.004zbMath1336.65167arXiv1501.05782OpenAlexW2053002875MaRDI QIDQ278351

Anotida Madzvamuse, Andy H. W. Chung

Publication date: 2 May 2016

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

Full work available at URL: https://arxiv.org/abs/1501.05782

zbMATH Keywords

reaction-diffusion systemsNewton methodbackward Euler methodCrank-Nicolson methodfractional-step \(\theta\) schemefully implicit time-stepping schemes

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (12)

Domain-Dependent Stability Analysis of a Reaction–Diffusion Model on Compact Circular Geometries ⋮ Classification of parameter spaces for a reaction-diffusion model on stationary domains ⋮ Numerical investigation based on a local meshless radial point interpolation for solving coupled nonlinear reaction-diffusion system ⋮ Constraint energy minimizing generalized multiscale finite element method for multi-continuum Richards equations ⋮ Prediction of numerical homogenization using deep learning for the Richards equation ⋮ CMMSE: Analysis of order reduction when Lawson methods integrate nonlinear initial boundary value problems ⋮ Arbitrary high-order unconditionally stable methods for reaction-diffusion equations with inhomogeneous boundary condition via deferred correction ⋮ Analysis and Simulations of Coupled Bulk-surface Reaction-Diffusion Systems on Exponentially Evolving Volumes ⋮ On the linear stability of some finite difference schemes for nonlinear reaction-diffusion models of chemical reaction networks ⋮ Turing pattern formation under heterogeneous distributions of parameters for an activator-depleted reaction model ⋮ Multiscale simulations for multi-continuum Richards equations ⋮ Stability Analysis and Parameter Classification of a Reaction-Diffusion Model on an Annulus

Uses Software

• deal.ii
• Chemotaxis

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