A second-order finite difference scheme for a class of singularly perturbed delay differential equations

DOI10.1080/00207160801989875zbMath1185.65135OpenAlexW2143987951MaRDI QIDQ5852132

Zhongdi Cen

Publication date: 26 January 2010

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160801989875

zbMATH Keywords

singular perturbationerror estimatesuniform convergencenumerical experimentsfinite difference schemeShishkin meshnonlinear delay differential equations

Mathematics Subject Classification ID

Related Items (11)

Layer-adapted methods for quasilinear singularly perturbed delay differential problems ⋮ A finite-difference scheme to approximate non-negative and bounded solutions of a FitzHugh–Nagumo equation ⋮ On some explicit non-standard methods to approximate nonnegative solutions of a weakly hyperbolic equation with logistic nonlinearity ⋮ A second order numerical method for singularly perturbed problem with non-local boundary condition ⋮ ROBUST NUMERICAL METHOD FOR SINGULARLY PERTURBED CONVECTION-DIFFUSION TYPE PROBLEMS WITH NON-LOCAL BOUNDARY CONDITION ⋮ A second order uniformly convergent numerical scheme for parameterized singularly perturbed delay differential problems ⋮ A robust numerical method for a two-parameter singularly perturbed time delay parabolic problem ⋮ Unnamed Item ⋮ Unnamed Item ⋮ A uniformly almost second order convergent numerical method for singularly perturbed delay differential equations ⋮ An efficient numerical method for coupled systems of singularly perturbed parabolic delay problems

Cites Work

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• Numerical treatment of boundary value problems for second order singularly perturbed delay differential equations
• A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations
• Stability and error analysis of one-leg methods for nonlinear delay differential equations
• The midpoint upwind scheme
• Asymptotic expansion for the solution of singularly perturbed delay differential equations
• Numerical solution of retarded functional differential equations as abstract Cauchy problems.
• Numerical solution of constant coefficient linear delay differential equations as abstract Cauchy problems
• \(\epsilon\)-uniformly convergent nonstandard finite difference methods for singularly perturbed differential difference equations with small delay
• A parameter-robust finite difference method for singularly perturbed delay parabolic partial differential equations
• Uniform numerical method for singularly perturbed delay differential equations
• Stability analysis of Runge-Kutta methods for systems of delay differential equations
• Uniformly convergent non-standard finite difference methods for singularly perturbed differential-difference equations with delay and advance
• Singular Perturbation Analysis of Boundary Value Problems for Differential-Difference Equations
• Oscillation and Chaos in Physiological Control Systems
• Numerical Methods for Delay Differential Equations
• Sufficient conditions for uniform convergence on layer-adapted grids
• Exponential fitting of the delayed recruitment/renewal equation

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