A new numerical algorithm for time-dependent singularly perturbed differential-difference convection-diffusion equation arising in computational neuroscience
DOI10.1007/s40314-022-02102-yOpenAlexW4309580825MaRDI QIDQ2678824
Publication date: 25 January 2023
Published in: Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s40314-022-02102-y
singular perturbationCrank-Nicolson methodparabolic problemdifferential-difference equationsparameter-uniform convergencemodified cubic B-splinesgeneralized Shishkin mesh
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Singular nonlinear boundary value problems for ordinary differential equations (34B16) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)
Cites Work
- Unnamed Item
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- Unnamed Item
- Parameter uniform numerical scheme for time dependent singularly perturbed convection-diffusion-reaction problems with general shift arguments
- A novel fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation
- A parameter-uniform numerical method for time-dependent singularly perturbed differential-difference equations
- A novel mathematical modeling of multiple scales for a class of two dimensional singular perturbed problems
- Delay differential equations: with applications in population dynamics
- A wavelet-Galerkin method for a singularly perturbed convection-dominated diffusion equation
- Numerical solutions of singularly perturbed one-dimensional parabolic convection-diffusion problems by the Bessel collocation method
- A uniformly convergent B-spline collocation method on a nonuniform mesh for singularly perturbed one-dimensional time-dependent linear convection-diffusion problem
- Combined finite volume element method for singularly perturbed reaction-diffusion problems
- A lower bound for the smallest singular value of a matrix
- Firing rates of motoneurons with strong random synaptic excitation
- A practical guide to splines
- A second order scheme for a time-dependent, singularly perturbed convection-diffusion equation
- An analysis of Stein's model for stochastic neuronal excitation
- B-spline collocation methods and their convergence for a class of nonlinear derivative dependent singular boundary value problems
- Higher order uniformly convergent numerical algorithm for time-dependent singularly perturbed differential-difference equations
- Solution of singularly perturbed differential difference equations and convection delayed dominated diffusion equations using Haar wavelet
- Wavelet-based approximation for two-parameter singularly perturbed problems with Robin boundary conditions
- A high-order numerical algorithm for solving Lane-Emden equations with various types of boundary conditions
- High order parameter-uniform discretization for singularly perturbed parabolic partial differential equations with time delay
- A parameter-robust finite difference method for singularly perturbed delay parabolic partial differential equations
- Numerical treatment for the class of time dependent singularly perturbed parabolic problems with general shift arguments
- \(\varepsilon \)-uniform numerical technique for the class of time dependent singularly perturbed parabolic problems with state dependent retarded argument arising from generalised Stein's model of neuronal variability
- Quintic B-spline collocation method for fourth order partial integro-differential equations with a weakly singular kernel
- Block-triangular preconditioning methods for linear third-order ordinary differential equations based on reduced-order sinc discretizations
- On the convergence of odd-degree spline interpolation
- On error bounds for spline interpolation
- Preconditioners for nonsymmetric block Toeplitz-like-plus-diagonal linear systems
- A uniformly convergent collocation method for singularly perturbed delay parabolic reaction-diffusion problem
- On sinc discretization and banded preconditioning for linear third-order ordinary differential equations
- A layer adaptive B-spline collocation method for singularly perturbed one-dimensional parabolic problem with a boundary turning point
- Robust Numerical Methods for Singularly Perturbed Differential Equations
- On Preconditioned Iterative Methods for Certain Time-Dependent Partial Differential Equations
- Higher order numerical approximation for time dependent singularly perturbed differential‐difference convection‐diffusion equations
- Numerical Methods for Delay Differential Equations
- On order-reducible sinc discretizations and block-diagonal preconditioning methods for linear third-order ordinary differential equations
- Trigonometric quinticB-spline collocation method for singularly perturbed turning point boundary value problems
- Matrix Analysis and Computations
- A higher-order scheme for quasilinear boundary value problems with two small parameters
- A higher order uniformly convergent method for singularly perturbed parabolic turning point problems
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