LDG method for reaction-diffusion dynamical systems with time delay

DOI10.1016/j.amc.2011.03.153zbMath1239.65062OpenAlexW2064887350MaRDI QIDQ547987

Dongfang Li, Hongyu Qin, Cheng-Jian Zhang

Publication date: 27 June 2011

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

Full work available at URL: https://doi.org/10.1016/j.amc.2011.03.153

zbMATH Keywords

stabilitynumerical resultserror estimateslocal discontinuous Galerkin methoddynamical systems with time delaysemi-linear reaction-diffusion

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Partial functional-differential equations (35R10) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Semilinear parabolic equations (35K58)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local discontinuous Galerkin methods for nonlinear dispersive equations
• Local discontinuous Galerkin finite element method and error estimates for one class of Sobolev equation
• A novel fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation
• Implicit-explicit predictor-corrector schemes for nonlinear parabolic differential equations
• Asymptotic stability of exact and discrete solutions for neutral multidelay-integro-differential equations
• Conditional contractivity of Runge-Kutta methods for nonlinear differential equations with many variable delays
• Oscillations and global attractivity in models of hematopoiesis
• Nonlinear parabolic-hyperbolic coupled systems and their attractors
• Traveling wavefront in a hematopoiesis model with time delay
• Nonlinear stability of discontinuous Galerkin methods for delay differential equations
• The extended one-leg methods for nonlinear neutral delay-integro-differential equations
• Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations
• Stable steady state of some population models
• The asymptotic stability of theoretical and numerical solutions for systems of neutral multidelay-differential equations
• Stability analysis of Runge-Kutta methods for nonlinear delay differential equations
• Theory and applications of partial functional differential equations
• Oscillation and global attractivity in hematopoiesis model with delay time
• A parameter-robust finite difference method for singularly perturbed delay parabolic partial differential equations
• Dynamics for a type of general reaction-diffusion model
• AN ANALYSIS OF THREE DIFFERENT FORMULATIONS OF THE DISCONTINUOUS GALERKIN METHOD FOR DIFFUSION EQUATIONS
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• A Local Discontinuous Galerkin Method for KdV Type Equations
• D-convergence and GDN-stability of Runge-Kutta methods for a class of delay systems
• Asymptotic behavior of multistep Runge-Kutta methods for systems of delay differential equations

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