An ε-uniform numerical method for third order singularly perturbed delay differential equations with discontinuous convection coefficient and source term

Subburayan, V.; Mahendran, Rakesh Kumar

doi:10.1016/j.amc.2018.03.036

Cited by 8 publications

(9 citation statements)

References 11 publications

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“…Furthermore, it is proved that, the present method is of almost first order convergence. In Subburayan and Mahendran (2018), the authors have applied fitted finite difference scheme with piecewise linear interpolation for Table 3 For fixed N = 32 and ε = 2 −6 , the iterations of u 2 of the Example 2…”

Section: Discussionmentioning

confidence: 99%

Asymptotic numerical method for third-order singularly perturbed convection diffusion delay differential equations

Subburayan

Mahendran

2020

Comp. Appl. Math.

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In this paper, an asymptotic numerical method based on a fitted finite difference scheme and the fourth-order Runge-Kutta method with piecewise cubic Hermite interpolation on Shishkin mesh is suggested to solve singularly perturbed boundary value problems for thirdorder ordinary differential equations of convection diffusion type with a delay. An error estimate is derived using the supremum norm and it is of almost first-order convergence. A nonlinear problem is also solved using the Newton's quasi linearization technique and the present asymptotic numerical method. Numerical results are provided to illustrate the theoretical results. Keywords Third-order differential equations • Convection diffusion equation • Boundary value problem • Singularly perturbed problem • Shishkin mesh • Delay differential equations • Asymptotic numerical methods Mathematics Subject Classification 34K10 • 34K26 • 34K28

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Section: Discussionmentioning

confidence: 99%

Asymptotic numerical method for third-order singularly perturbed convection diffusion delay differential equations

Subburayan

Mahendran

2020

Comp. Appl. Math.

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“…where is very-very small positive number and a(x), f(x) are discontinuous functions as shown below: (Subburayan and Mahendran, 2018).…”

Section: Problem Statementmentioning

confidence: 99%

“…It is apparent that ̅ satisfy ( 1)-( 2) and the constants A and B can be obtained by procedure given by Subburayan and Mahendran (2018) to show existence of the solution.…”

Section: Existence Of Solutionmentioning

confidence: 99%

Quintic B-Spline Technique for Numerical Treatment of Third Order Singular Perturbed Delay Differential Equation

Vaid¹,

Arora²

2019

Int J Math, Eng, Manag Sci

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In this paper, a class of third order singularly perturbed delay differential equation with large delay is considered for numerical treatment. The considered equation has discontinuous convection-diffusion coefficient and source term. A quintic trigonometric B-spline collocation technique is used for numerical simulation of the considered singularly perturbed delay differential equation by dividing the domain into the uniform mesh. Further, uniform convergence of the solution is discussed by using the concept of Hall error estimation and the method is found to be of first-order convergent. The existence of the solution is also established. Computation work is carried out to validate the theoretical results.

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“…In recent years, both mathematicians and physicists have devoted remarkable effort to the study of numerical solutions of singularly perturbed delay differential equations with discontinuous data and large delay parameter. For instance, in [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , the authors suggested different numerical methods for solving singularly perturbed ordinary differential equations with discontinuous coefficients and large delay parameter using fitting techniques. Mukherjee and Natesan [24] developed the implicit upwind finite difference scheme on Shishkin-type meshes for a class of singularly perturbed parabolic convection-diffusion problems exhibiting strong interior layers.…”

Section: Introductionmentioning

confidence: 99%

Computational method for singularly perturbed parabolic differential equations with discontinuous coefficients and large delay

Daba

Duressa

2022

Heliyon

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An ε-uniform numerical method for third order singularly perturbed delay differential equations with discontinuous convection coefficient and source term

Cited by 8 publications

References 11 publications

Asymptotic numerical method for third-order singularly perturbed convection diffusion delay differential equations

Asymptotic numerical method for third-order singularly perturbed convection diffusion delay differential equations

Quintic B-Spline Technique for Numerical Treatment of Third Order Singular Perturbed Delay Differential Equation

Computational method for singularly perturbed parabolic differential equations with discontinuous coefficients and large delay

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