Hyperbolic partial differential-difference equation in the mathematical modeling of neuronal firing and its numerical solution

DOI10.1016/j.amc.2007.12.051zbMath1155.65374OpenAlexW2008918176WikidataQ115361774 ScholiaQ115361774MaRDI QIDQ945242

Kapil K. Sharma, Param Jeet Singh

Publication date: 12 September 2008

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

Full work available at URL: https://doi.org/10.1016/j.amc.2007.12.051

zbMATH Keywords

finite differenceupwind schemedifferential-difference equationhyperbolic partial differential equationneuronal firing

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

Related Items (13)

Finite volume approximations for size structured neuron model ⋮ The method of lines for hyperbolic stochastic functional partial differential equations ⋮ An efficient hybrid method based on cubic B-spline and fourth-order compact finite difference for solving nonlinear advection-diffusion-reaction equations ⋮ Alternative direction implicit method for solving first order 2D hyperbolic delay differential equations ⋮ Applying cubic B-spline quasi-interpolation to solve 1D wave equations in polar coordinates ⋮ Higher-order MUSCL scheme for transport equation originating in a neuronal model ⋮ A stable noniterative prediction/correction domain decomposition method for hyperbolic problems ⋮ Numerical solution of Burgers-Fisher equation by cubic B-spline quasi-interpolation ⋮ Second-order treatment of the interface of domain decomposition method for parabolic problems ⋮ Numerical solution of first-order hyperbolic partial differential-difference equation with shift ⋮ FREEZING OF BIOLOGICAL TISSUES DURING CRYOSURGERY USING HYPERBOLIC HEAT CONDUCTION MODEL ⋮ Finite difference methods with interpolation for first-order hyperbolic delay differential equations ⋮ High-order upwind finite volume element schemes for modelling of neuronal firing

Cites Work

• Numerical approximation of hyperbolic systems of conservation laws
• Numerical treatment of partial differential equations. Revised translation of the 3rd German edition of `Numerische Behandlung partieller Differentialgleichungen' by Martin Stynes.
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