Parameter uniform numerical method for fourth order singularly perturbed turning point problems exhibiting boundary layers

Geetha, N.; Tamilselvan, A.

doi:10.1016/j.asej.2016.04.018

Cited by 5 publications

(3 citation statements)

References 18 publications

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“…It is a computationally proficient technique and the algorithm can easily be applied on a computer. The results obtained through this method are better than the existing method [7] with the same number of nodal points.…”

Section: Discussionmentioning

confidence: 83%

“…Example 5.4. Consider the following singular perturbation boundary value problem [7]: −εy iv (t) + 5ty (t) + (4 + t) y (t) + 2y 2 (t) = 0, t ∈ [−1, 1] , y (−1) = 1, y (1) = 1, y (−1) = 2, y (1) = 2.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Sarakhsi et al [25] have studied the existence of boundary layer problem. Parameter uniform numerical scheme to solve fourth order singularly perturbed turning points problems have been presented by Geetha and Tamilselvan [7]. Sharma et al [26] have done the survey on singularly perturbed turning point and interior layers problem.…”

Section: Introductionmentioning

confidence: 99%

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Quintic B-spline method for numerical solution of fourth order singular perturbation boundary value problems

Lodhi

Mishra

2018

Stud. Univ. Babes-Bolyai Math.

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In this communication, we have studied an efficient numerical approach based on uniform mesh for the numerical solutions of fourth order singular perturbation boundary value problems. Such type of problems arises in various fields of science and engineering, like electrical network and vibration problems with large Peclet numbers, Navier-Stokes flows with large Reynolds numbers in the theory of hydrodynamics stability, reaction-diffusion process, quantum mechanics and optimal control theory etc. In the present study, a quintic B-spline method has been discussed for the approximate solution of the fourth order singular perturbation boundary value problems. The convergence analysis is also carried out and the method is shown to have convergence of second order. The performance of present method is shown through some numerical tests. The numerical results are compared with other existing method available in the literature. (2010): 65L10. Keywords: Fourth order singular perturbation boundary value problem, quintic B-spline, quasilinearization, uniform mesh, convergence analysis. y (a) = η 1 , y (b) = η 2 , y (a) = η 3 , y (b) = η 4 . Mathematics Subject Classification(1.2) where η 1 , η 2 , η 3 and η 4 are finite real constants and ε is a small positive parameter, such that 0 < ε 1. Moreover, we assume that the functions p (t) ,q (t) ,r (t) and f (t) are sufficiently smooth. Further, the problem (1.1) is called non-turning point problem if p (t) ≥ α > 0 throughout the interval [a, b], where α is some positive constant and boundary layer will be in the neighbourhood of t = a [9]. In the same

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Section: Discussionmentioning

confidence: 83%

Section: Numerical Resultsmentioning

confidence: 99%