A finite-difference method for a singularly perturbed delay integro-differential equation

DOI10.1016/j.cam.2016.06.018zbMath1346.65076OpenAlexW2460998628WikidataQ115359815 ScholiaQ115359815MaRDI QIDQ738989

Gabil M. Amiraliyev, Mustafa Kudu, Ilhame Amirali

Publication date: 16 August 2016

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

Full work available at URL: https://doi.org/10.1016/j.cam.2016.06.018

zbMATH Keywords

numerical examplesingular perturbationuniform convergenceerror estimationinitial value problemquadrature rulesdelay difference schemelayer adapted meshlinear first-order Volterra integro-differential equation

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Volterra integral equations (45D05) Linear integral equations (45A05)

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Cites Work

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• Delay-dependent stability analysis of symmetric boundary value methods for linear delay integro-differential equations
• A brief survey on numerical methods for solving singularly perturbed problems
• Numerical solution of a singularly perturbed Volterra integro-differential equation
• Uniform difference method for singularly perturbed Volterra integro-differential equations
• Stability of linear multistep methods for delay integro-differential equations
• Integrodifferential inequality for stability of singularly perturbed impulsive delay integrodifferential equations
• Singular perturbation methods for ordinary differential equations
• A survey of singularly perturbed Volterra equations
• Stability analysis of Volterra delay-integro-differential equations and their backward differentiation time discretization.
• Stability of Runge-Kutta methods for delay integro-differential equations
• Superconvergent interpolants for collocation methods applied to Volterra integro-differential equations with delay
• Singularly perturbed integro-differential equations with diagonal degeneration of the kernel in reverse time
• Numerical modelling in biosciences using delay differential equations
• Qualitative behaviour of numerical approximations to Volterra integro-differential equations
• Mathematical modelling of the intravenous glucose tolerance test
• Dissipativity of \(\theta\)-methods for nonlinear Volterra delay-integro-differential equations
• Errors of linear multistep methods for singularly perturbed Volterra delay-integro-differential equations
• The role of delays in innate and adaptive immunity to intracellular bacterial infection
• Numerical solutions of integral and integro-differential equations using Legendre polynomials
• Uniform numerical method for singularly perturbed delay differential equations
• Difference schemes of exponential type for singularly perturbed Volterra integro-differential problems
• Singularly Perturbed Volterra Integro-differential Equations
• A nonlinear singularly perturbed Volterra integrodifferential equation occurring in polymer rheology
• Numerical solution of delay integro‐differential equations by using Taylor collocation method

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