Fitted numerical methods for singularly perturbed one-dimensional parabolic partial differential equations with small shifts arising in the modelling of neuronal variability

DOI10.1007/S12591-017-0363-9zbMath1416.65280OpenAlexW2613615557MaRDI QIDQ2415422

R. Nageshwar Rao, P. Pramod Chakravarthy

Publication date: 21 May 2019

Published in: Differential Equations and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12591-017-0363-9

zbMATH Keywords

singular perturbationsconvection-diffusionparabolic partial differential equationexponentially fitted method

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Neural biology (92C20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) 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)

Related Items (12)

UNIFORMLY CONVERGENT NUMERICAL METHOD FOR SINGULARLY PERTURBED DELAY PARABOLIC DIFFERENTIAL EQUATIONS ARISING IN COMPUTATIONAL NEUROSCIENCE ⋮ Quadratic B‐spline collocation method for time dependent singularly perturbed differential‐difference equation arising in the modeling of neuronalactivity ⋮ Parameter uniform fitted mesh finite difference scheme for elliptical singularly perturbed problems with mixed shifts in two dimensions ⋮ A REPRODUCING KERNEL METHOD FOR SOLVING SINGULARLY PERTURBED DELAY PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS ⋮ A uniformly convergent defect correction method for parabolic singular perturbation problems with a large delay ⋮ Unnamed Item ⋮ Unnamed Item ⋮ A Tension Spline Based Numerical Algorithm for Singularly Perturbed Partial Differential Equations on Non-uniform Discretization ⋮ Unnamed Item ⋮ Uniformly convergent hybrid numerical method for singularly perturbed delay convection-diffusion problems ⋮ A stable finite difference scheme and error estimates for parabolic singularly perturbed PDEs with shift parameters ⋮ Fitted Numerical Scheme for Solving Singularly Perturbed Parabolic Delay Partial Differential Equations

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