A Green's function formulation of nonlocal finite-difference schemes for reaction-diffusion equations

DOI10.1016/j.cam.2010.10.015zbMath1210.65156OpenAlexW1971633872MaRDI QIDQ631916

Eliseo Hernandez-Martinez, Francisco J. Valdés-Parada, José de Jesús Álvarez-Ramírez

Publication date: 14 March 2011

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

Full work available at URL: https://doi.org/10.1016/j.cam.2010.10.015

zbMATH Keywords

Green's functionnumerical examplesdomain decompositionreaction-diffusion equationsnon-standard finite difference method

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Integral representations of solutions to PDEs (35C15) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)

Related Items (6)

Ordinary and generalized Green's functions for the second order discrete nonlocal problems ⋮ Coupling finite volume and nonstandard finite difference schemes for a singularly perturbed Schrödinger equation ⋮ A Green's function approach for the numerical solution of a class of fractional reaction-diffusion equations ⋮ Nonstandard finite difference methods: recent trends and further developments ⋮ GREEN’S MATRICES FOR FIRST ORDER DIFFERENTIAL SYSTEMS WITH NONLOCAL CONDITIONS∗ ⋮ Positive numerical solution for a nonarbitrage liquidity model using nonstandard finite difference schemes

Cites Work

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• Non-standard finite-differences schemes for generalized reaction-diffusion equations
• Qualitatively stable finite difference schemes for advection--reaction equations.
• On non-standard finite difference models of reaction-diffusion equations
• Discretizations of nonlinear differential equations using explicit nonstandard methods
• Contributions to the mathematics of the nonstandard finite difference method and applications
• Construction of a Finite-Difference Scheme that Exactly Conserves Energy for a Mixed Parity Oscillator

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