A numerical method based on finite difference for boundary value problems for singularly perturbed delay differential equations

Kadalbajoo, Mohan K.; Sharma, Kapil K.

doi:10.1016/j.amc.2007.08.089

Cited by 68 publications

(57 citation statements)

References 6 publications

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“…Kadalbajoo, et al [18] discussed a boundary value problem for a second-order singularly perturbed delay differential equation. When the delay argument is sufficiently small, to tackle the delay term, the researchers used Taylor's series expansion and presented an asymptotic as well as numerical approach to solve such kind of boundary value problems.…”

Section: New Research Directionsmentioning

confidence: 99%

Recent progress in study of singular perturbation problems

Jia-Qi

2009

J. Shanghai Univ.(Engl. Ed.)

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Some results for the singular perturbation theory, methods and applications in the new century are reviewed in this paper. It could be found that in the recent decade, many approximate methods have been developed and refined, including the method of averaging, boundary layer methods, methods of matched asymptotic expansion and methods of multiple scales. An overview is given on the new work about various problems, such as the reaction diffusion, turning points, boundary layers, shock waves, stability problem, solitons, attractors, canard solution, scattering light wave and neuron network, etc. And then, a great number of applied problems are solved in applied and astrnatics and so on, from which only some examples are extracted and described in this review.

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Section: New Research Directionsmentioning

confidence: 99%

Recent progress in study of singular perturbation problems

Jia-Qi

2009

J. Shanghai Univ.(Engl. Ed.)

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“…But in the recent years, there has been growing interest in this area. In fact, Fevzi Erdogan [4] proposed an exponentially fitted operator method for singularly perturbed first order delay differential equations, Kadalbajoo and Sharma [5]- [7] and Jugal Mohapatra and Natesan [8] proposed few numerical methods for SPDDEs with small delays. Subburayan and Ramanujam [9]- [14] suggested numerical methods named as initial value technique and asymptotic numerical method for singularly perturbed delay differential equations of reaction-diffusion type as well as convection-diffusion type.…”

Section: Introductionmentioning

confidence: 99%

An iterative numerical method for singularly perturbed reaction–diffusion equations with negative shift

Selvi

Ramanujam

2016

Journal of Computational and Applied Mathematics

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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%