Numerical analysis of singularly perturbed delay differential equations with layer behavior

Kadalbajoo, Mohan K.; Sharma, Kapil K.

doi:10.1016/j.amc.2003.06.012

Cited by 82 publications

(52 citation statements)

References 9 publications

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“…There, the biologist Hutchinson [4] states 'There is a tendency for the time lag to be reduced as much as possible by natural selection'. Further studies of the effect of on the layer behaviour of the solution has been carried out by Kadalbajoo and Sharma [5]. Similar observations have been made by the same authors when is also present [6].…”

Section: Y (X) + A(x)y(x − ) + W(x)y(x) + B(x)y(xsupporting

confidence: 67%

Uniformly convergent non-standard finite difference methods for singularly perturbed differential-difference equations with delay and advance

Patidar

Sharma²

2006

Int. J. Numer. Meth. Engng

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SUMMARYA new class of fitted operator finite difference methods are constructed via non-standard finite difference methods ((NSFDM)s) for the numerical solution of singularly perturbed differential difference equations having both delay and advance arguments. The main idea behind the construction of our method(s) is to replace the denominator function of the classical second-order derivative with a positive function derived systematically in such a way that it captures significant properties of the governing differential equation and thus provides the reliable numerical results. Unlike other FOFDMs constructed in standard ways, the methods that we present in this paper are fairly simple to construct (and thus enrich the class of fitted operator methods by adding these new methods). These methods are shown to be -uniformly convergent with order two which is the highest possible order of convergence obtained via any fitted operator method for the problems under consideration. This paper further clarifies several doubts, e.g. why a particular scheme is not suitable for the whole range of values of the associated parameters and what could be the possible remedies. Finally, we provide some numerical examples which illustrate the theoretical findings.

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Section: Y (X) + A(x)y(x − ) + W(x)y(x) + B(x)y(xsupporting

confidence: 67%

Uniformly convergent non-standard finite difference methods for singularly perturbed differential-difference equations with delay and advance

Patidar

Sharma²

2006

Int. J. Numer. Meth. Engng

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“…In recent years, the integral and integro-differential equations have a major role in engineering, mechanics, physics, chemistry, astronomy, biology, economics, potential theory, electrostatics, ( Kadalbajoo & Sharma 2004). A physical event can be modeled by these equations.…”

Section: Introductionmentioning

confidence: 99%

Fibonacci collocation method with a residual error Function to solve linear Volterra integro differential equations

Bahşı¹

2016

ntmsci

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In this paper, a new collocation method based on the Fibonacci polynomials is introduced to solve the high-order linear Volterraintegro-differential equations under the conditions. Numerical examples are included to demonstrate the applicability and validity of the proposed method and comparisons are made with the existing results. In addition, an error estimation based on the residual functions is presented for this method. The approximate solutions are improved by using this error estimation.

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“…Lange and Miura [1] initiated the singular perturbation analysis of boundary value problems for differential difference equations with small shifts. The numerical study of second order singularly perturbed delay differential equations has been given in [2][3] and references therein. In this paper, we present an exponentially fitted method on uniform mesh based on cubic spline method for the convection delayed dominated diffusion equation.…”

Section: Introductionmentioning

confidence: 99%

The numerical simulation of convection delayed dominated diffusion equation

Kumar

Kanth

2016

MATEC Web of Conferences

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Numerical analysis of singularly perturbed delay differential equations with layer behavior

Cited by 82 publications

References 9 publications

Uniformly convergent non-standard finite difference methods for singularly perturbed differential-difference equations with delay and advance

Uniformly convergent non-standard finite difference methods for singularly perturbed differential-difference equations with delay and advance

Fibonacci collocation method with a residual error Function to solve linear Volterra integro differential equations

The numerical simulation of convection delayed dominated diffusion equation

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