Singularly perturbed delay differential equations of convection–diffusion type with integral boundary condition

Sekar, Elango; Tamilselvan, A.

doi:10.1007/s12190-018-1198-4

Cited by 38 publications

(24 citation statements)

References 16 publications

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“…For the proof refer [16] The following theorem shows the parameter uniform convergence of the scheme developed. Remark: A similar analysis for convergence may be carried out for finite difference scheme (24).…”

Section: Case (Iv)mentioning

confidence: 97%

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Exponentially fitted finite difference method for singularly perturbed delay differential equations with integral boundary condition

Debela

Duressa

2019

International Journal of Engineering and Applied Sciences

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In this paper, exponentially fitted finite difference method for solving singularly perturbed delay differential equation with integral boundary condition is considered. To treat the integral boundary condition, Simpson's rule is applied. The stability and parameter uniform convergence of the proposed method are proved. To validate the applicability of the scheme, two model problems are considered for numerical experimentation and solved for different values of the perturbation parameter,  and mesh size, .h The numerical results are tabulated in terms of maximum absolute errors and rate of convergence and it is observed that the present method is more accurate and  -uniformly convergent for h   where the classical numerical methods fails to give good result and it also improves the results of the methods existing in the literature.

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Section: Case (Iv)mentioning

confidence: 97%

“…For small values of ,  the boundary value problem (1)-(3) exhibits strong boundary layer at 2 x  and interior layer at 1 x  (see [16]) and cannot, in general, be solved analytically because of the dependence of ( ), ( ) and ( ) a x b x c x on the spatial coordinate .…”

Section: Formulation Of the Numerical Schemementioning

confidence: 99%

Exponentially fitted finite difference method for singularly perturbed delay differential equations with integral boundary condition

Debela

Duressa

2019

International Journal of Engineering and Applied Sciences

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“…Now using Taylor's series for y i and y i+1 up to first term and substituting the results in equation (17) into equation (14) and simplifying, the exponential fitting factor is obtained as…”

Section: Formulation Of the Methodsmentioning

confidence: 99%

“…erefore, it is important to develop a numerical method that gives good results for small values of the perturbation parameter where others fails to give good result and convergent independent of the values of the perturbation parameter. In recent years, the authors [11][12][13][14][15] have developed various numerical schemes on uniform meshes for singularly perturbed first and second order differential equations with integral boundary conditions. As far as the researchers' knowledge is concerned numerical solution of the singularly perturbed boundary value problem containing integral boundary condition via the accelerated exponential fitted operator method is first being considered.…”

Section: Introductionmentioning

confidence: 99%

Accelerated Exponentially Fitted Operator Method for Singularly Perturbed Problems with Integral Boundary Condition

Debela

Duressa

2020

International Journal of Differential Equations

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In this paper, we consider a class of singularly perturbed differential equations of convection diffusion type with integral boundary condition. An accelerated uniformly convergent numerical method is constructed via exponentially fitted operator method using Richardson extrapolation techniques and numerical integration methods to solve the problem. e integral boundary condition is treated using numerical integration techniques. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. e method is shown to be ε-uniformly convergent.

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“…Therefore, it is necessary to improve suitable numerical methods which are uniformly convergent to solve the problem. Some authors have worked on singularly perturbed differential equations with delay using uniformly convergent numerical methods [1][2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Third order singularly perturbed delay differential equation of reaction diffusion type with integral boundary condition

Sekar¹,

Tamilselvan²

2019

J. Appl. Math. Comput. Mech.

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A class of third order singularly perturbed delay differential equations of reaction diffusion type with an integral boundary condition is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The method suggested is of almost first order convergent. An error estimate is derived in the discrete norm. Numerical examples are presented, which validate the theoretical estimates.

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Singularly perturbed delay differential equations of convection–diffusion type with integral boundary condition

Cited by 38 publications

References 16 publications

Exponentially fitted finite difference method for singularly perturbed delay differential equations with integral boundary condition

Exponentially fitted finite difference method for singularly perturbed delay differential equations with integral boundary condition

Accelerated Exponentially Fitted Operator Method for Singularly Perturbed Problems with Integral Boundary Condition

Third order singularly perturbed delay differential equation of reaction diffusion type with integral boundary condition

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