Singular Perturbation Analysis of Boundary Value Problems for Differential-Difference Equations

DOI10.1137/0142036zbMath0515.34058OpenAlexW2070043289MaRDI QIDQ3661953

Charles G. Lange, Robert M. Miura

Publication date: 1982

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0142036

zbMATH Keywords

approximate solutionshave small parameterssecond-order linear differential difference equations

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Boundary value problems for functional-differential equations (34K10)

Related Items (only showing first 100 items - show all)

A novel fitted method for a class of singularly perturbed differential-difference equations with small delay exhibiting twin layer or oscillatory behaviour ⋮ Analysis of a Hybrid Numerical Scheme for Singularly Perturbed Convection-Diffusion Type Delay Problems ⋮ Asymptotic streamline diffusion finite element method for singularly perturbed convection–diffusion differential difference equations ⋮ Analysis of the SDFEM for singularly perturbed differential-difference equations ⋮ A fitted numerical scheme for second order singularly perturbed delay differential equations via cubic spline in compression ⋮ A parameter uniform numerical method for singularly perturbed delay problems with discontinuous convection coefficient ⋮ Numerical analysis of singularly perturbed delay differential equations with layer behavior ⋮ Standing pulse-like solutions of a spatially aggregating population model ⋮ Singularly perturbed nonlinear boundary value problem for a kind of Volterra type functional differential equation ⋮ Singularly perturbed boundary value problems for semi-linear retarded differential equations with nonlinear boundary conditions ⋮ Exponential methods for singularly perturbed ordinary differential-difference equations ⋮ Maximum norm a posteriori error estimates for a singularly perturbed differential difference equation with small delay ⋮ Unnamed Item ⋮ An initial value technique for singularly perturbed convection-diffusion problems with a negative shift ⋮ Asymptotic and numerical analysis of singular perturbation problems: A survey ⋮ A numerical approach for solving singularly perturbed convection delay problems via exponentially fitted spline method ⋮ Hybrid method for numerical solution of singularly perturbed delay differential equations ⋮ Unnamed Item ⋮ Numerical study of time delay singularly perturbed parabolic differential equations involving both small positive and negative space shifts ⋮ A new stable finite difference scheme and its convergence for time-delayed singularly perturbed parabolic PDEs ⋮ Robust numerical method for space shift 2D singularly perturbed parabolic convection diffusion differential equations ⋮ Exponentially fitted tension spline method for singularly perturbed differential difference equations ⋮ A second order stabilized central difference method for singularly perturbed differential equations with a large negative shift ⋮ Uniformly convergent finite difference method for reaction-diffusion type third order singularly perturbed delay differential equation ⋮ Parameter robust higher‐order finite difference method for convection‐diffusion problem with time delay ⋮ Analysis of a numerical technique for a singularly perturbed parabolic convection–diffusion interface problem with time delay ⋮ Quadratic B‐spline collocation method for time dependent singularly perturbed differential‐difference equation arising in the modeling of neuronalactivity ⋮ A parameter-uniform numerical scheme for solving singularly perturbed parabolic reaction-diffusion problems with delay in the spatial variable ⋮ Uniformly convergent hybrid numerical scheme for singularly perturbed turning point problems with delay ⋮ Parameter uniform fitted mesh finite difference scheme for elliptical singularly perturbed problems with mixed shifts in two dimensions ⋮ Numerical approximation for a class of singularly perturbed delay differential equations with boundary and interior layer(s) ⋮ Uniform convergence method for a delay differential problem with layer behaviour ⋮ Error analysis of a weak Galerkin finite element method for singularly perturbed differential-difference equations ⋮ A higher order compact numerical approach for singularly perturbed parabolic problem with retarded term ⋮ An iterative numerical method for singularly perturbed reaction-diffusion equations with negative shift ⋮ Numerical study of singularly perturbed differential-difference equation arising in the modeling of neuronal variability ⋮ Numerical analysis of singularly perturbed delay differential turning point problem ⋮ A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations ⋮ Higher order numerical approximation for time dependent singularly perturbed differential‐difference convection‐diffusion equations ⋮ A parameter-uniform numerical method for time-dependent singularly perturbed differential-difference equations ⋮ Unnamed Item ⋮ Analysis of a higher order uniformly convergent method for singularly perturbed parabolic delay problems ⋮ Singularly Perturbed Delay Differential Equations and Numerical Methods ⋮ A Numerical Method for a System of Singularly Perturbed Differential Equations of Reaction-Diffusion Type with Negative Shift ⋮ A Parameter Uniform Numerical Method for an Initial Value Problem for a System of Singularly Perturbed Delay Differential Equations with Discontinuous Source Terms ⋮ Unnamed Item ⋮ Power spectra and dynamical invariants for delay-differential and difference equations ⋮ Singular Perturbation Analysis of Integral Equations ⋮ Numerical solution of singularly perturbed delay differential equations with layer behavior ⋮ A review on singularly perturbed differential equations with turning points and interior layers ⋮ Singular perturbation solution of boundary-value problem for a second- order differential-difference equation ⋮ An Adaptive Mesh Selection Strategy for Solving Singularly Perturbed Parabolic Partial Differential Equations with a Small Delay ⋮ Fitted finite difference method for singularly perturbed delay differential equations ⋮ A numerical method for solving singularly perturbed differential-difference equation arising in the modeling of neuronal variability ⋮ Comparative study on numerical methods for singularly perturbed advanced-delay differential equations ⋮ A novel method for singularly perturbed delay differential equations of reaction-diffusion type ⋮ Uniformly convergent numerical method for a singularly perturbed differential difference equation with mixed type ⋮ Upwind and midpoint upwind difference methods for time-dependent differential difference equations with layer behavior ⋮ Parameter-Robust Numerical Scheme for Time-Dependent Singularly Perturbed Reaction–Diffusion Problem with Large Delay ⋮ Parameter-uniform numerical treatment of singularly perturbed initial-boundary value problems with large delay ⋮ Unnamed Item ⋮ Uniform numerical method for singularly perturbed delay differential equations ⋮ A collocation method for singularly perturbed differential-difference turning point problems exhibiting boundary/interior layers ⋮ Renormalization group approach to a class of singularly perturbed delay differential equations ⋮ Solution of singularly perturbed differential-difference equations with mixed shifts using Galerkin method with exponential fitting ⋮ Parameter uniform method for a singularly perturbed system of delay differential equations of reaction-diffusion type with integral boundary conditions ⋮ On singularly perturbed retarded functional differential equations ⋮ Numerical treatment of a mathematical model arising from a model of neuronal variability ⋮ Uniformly convergent finite difference schemes for singularly perturbed convection diffusion type delay differential equations ⋮ Higher order uniformly convergent numerical algorithm for time-dependent singularly perturbed differential-difference equations ⋮ Asymptotic initial value technique for singularly perturbed convection-diffusion delay problems with boundary and weak interior layers ⋮ A parameter uniform numerical method for a singularly perturbed two-parameter delay differential equation ⋮ Numerical method for a singularly perturbed convection-diffusion problem with delay ⋮ Asymptotic analysis of the Hermite polynomials from their differential–difference equation ⋮ Higher-order uniformly convergent numerical scheme for singularly perturbed differential difference equations with mixed small shifts ⋮ Numerical solution of second order singularly perturbed delay differential equations via cubic spline in tension ⋮ Singular Perturbation Analysis of Boundary Value Problems for Differential‐Difference Equations. IV. A Nonlinear Example with Layer Behavior ⋮ Singularly Perturbed Convection-Diffusion Turning Point Problem with Shifts ⋮ NUMERICAL SOLUTION OF A BOUNDARY VALUE PROBLEM INCLUDING BOTH DELAY AND BOUNDARY LAYER ⋮ A NUMERICAL SCHEME FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS OF CONVECTION-DIFFUSION TYPE ON AN ADAPTIVE GRID ⋮ Solution with an internal transition layer for a singularly perturbed second-order equation with an advancing and a retarded argument ⋮ A novel approach for the numerical approximation to the solution of singularly perturbed differential-difference equations with small shifts ⋮ Numerical analysis of boundary-value problems for singularly-perturbed differential-difference equations with small shifts of mixed type ⋮ Numerical analysis of boundary-value problems for singularly perturbed differential-difference equations: small shifts of mixed type with rapid oscillations ⋮ An ϵ-uniform fitted operator method for solving boundary-value problems for singularly perturbed delay differential equations: Layer behavior ⋮ A class of finite difference schemes for singularly perturbed delay differential equations of second order ⋮ Uniformly convergent numerical method for singularly perturbed differential-difference equation using grid equidistribution ⋮ Singularly perturbed delay differential equations of convection-diffusion type with integral boundary condition ⋮ A kind of singularly perturbed boundary value problem for nonlinear Volterra functional-differential equations ⋮ THE PARAMETER-ROBUST NUMERICAL METHOD BASED ON DEFECT-CORRECTION TECHNIQUE FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH LAYER BEHAVIOR ⋮ Uniform difference method for parameterized singularly perturbed delay differential equations ⋮ A finite difference scheme for a class of singularly perturbed initial value problems for delay differential equations ⋮ Second order singularly perturbed delay differential equations with non-local boundary condition ⋮ A hybrid numerical scheme for singular perturbation delay problems with integral boundary condition ⋮ A second-order finite difference scheme for a class of singularly perturbed delay differential equations ⋮ Unnamed Item ⋮ A balanced norm error estimation for the time-dependent reaction-diffusion problem with shift in space ⋮ A first-order convergent parameter-uniform numerical method for a singularly perturbed second-order delay-differential equation of reaction-diffusion type with a discontinuous source term ⋮ Fitted numerical method with linear interpolation for third-order singularly perturbed delay problems ⋮ On discontinuous Galerkin finite element method for singularly perturbed delay differential equations

This page was built for publication: Singular Perturbation Analysis of Boundary Value Problems for Differential-Difference Equations