An ADI Method for Hysteretic Reaction-Diffusion Systems

DOI10.1137/S0036142994270181zbMath0873.65086MaRDI QIDQ4340785

Chichia Chiu, Noel J. Walkington

Publication date: 12 June 1997

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

hysteresisstabilityconvergencefinite difference methodreaction-diffusion equationsADI methodsmicrobiologyalternating-direction implicit methodgrowth of bacterial cellsaccretion pattern formation

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Iterative numerical methods for linear systems (65F10)

Related Items (7)

Convergence analysis and error estimate of second-order implicit–explicit scheme for Gray-Scott model ⋮ A nonoscillatory second-order time-stepping procedure for reaction-diffusion equations ⋮ Stability and Error Estimates of Fully Discrete Schemes for the Brusselator System ⋮ Adaptive optimal \(m\)-stage Runge-Kutta methods for solving reaction-diffusion-chemotaxis systems ⋮ An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems on evolving domains ⋮ A method to solve the reaction-diffusion-chemotaxis system ⋮ Maximum norm error bounds of ADI and compact ADI methods for solving parabolic equations

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