Open AccessDOI
Numerical Solution of Singularly Perturbed Delay Reaction-Diffusion Equations with Layer or Oscillatory Behaviour
Gemechis File,Gashu Gadisa,Tesfaye Aga,Y. N. Reddy +3 more
- Vol. 5, Iss: 1, pp 1-10
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In this paper, a numerical method for singularly perturbed delay differential equations with layer or oscillatory behavior for which a small shift (δ) is in the reaction term is presented.Abstract:
In this paper, we presented numerical method for solving singularly perturbed delay differential equations with layer or oscillatory behaviour for which a small shift (δ) is in the reaction term. First, the given singularly perturbed delay reaction-diffusion equation is converted into an asymptotically equivalent singularly perturbed two point boundary value problem and then solved by using fourth order finite difference method. The stability and convergence of the method has been investigated. The numerical results have been tabulated and further to examine the effect of delay on the boundary layer and oscillatory behavior of the solution, graphs have been given for different values of δ. Both theoretical and numerical rate of convergence have been established and are observed to be in agreement for the present method. Briefly, the present method improves the findings of some existing numerical methods in the literature.read more
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Journal ArticleDOI
Solution of Second Order Singular Perturbed Delay Differential Equation Using Trigonometric B-Spline
Mandeep Kaur Vaid,Geeta Arora +1 more
TL;DR: In this article, a numerical technique is presented to approximate the solution of a singular perturbed delay differential equation, which is based on trigonometric cubic B-spline functions in which derivatives are approximated as a linear sum of basis functions.
Journal ArticleDOI
A review on singular perturbed delay differential equations
Mandeep Kaur,Geeta Arora +1 more
TL;DR: In this paper, the authors present a survey of singular perturbed delay differential equations (SPDEs) and their application in control theory, elasticity, fluid mechanics, and biosciences.
Journal ArticleDOI
Numerical treatment of singularly perturbed delay reaction-diffusion equations
TL;DR: In this paper, a uniform convergent numerical method for solving singularly perturbed delay reaction-diffusion equations is presented, where the stability and convergence analysis are investigated, and the effect of the layer on the solution is examined.
Journal ArticleDOI
Exponentially Fitted Numerical Method for Singularly Perturbed Differential-Difference Equations
TL;DR: In this article, a numerical method to solve singularly perturbed differential-difference equations is presented, which exhibits layer or oscillatory behavior depending on the sign of the sum of the coefficients in reaction terms.
Journal ArticleDOI
Fitted Fourth Order Scheme for Singularly Perturbed Delay Convection-Diffusion Equations
Gashu Gadisa,Gemechis File +1 more
TL;DR: In this paper, a fitted fourth order numerical scheme for singularly perturbed convection-diffusion equations is presented and the obtained scheme is transformed into a three-term recurrence relation and solved by Thomas algorithm.
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