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01.09.2017

A numerical approach for solving singularly perturbed convection delay problems via exponentially fitted spline method

verfasst von: Ravi Kanth Adivi Sri Venkata, Murali Mohan Kumar Palli

Erschienen in: Calcolo | Ausgabe 3/2017

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Abstract

In this paper an exponentially fitted spline method is presented for solving singularly perturbed convection delay problems with boundary layer at left (or right) end of the domain. The error analysis of the scheme is investigated. It is shown that the proposed scheme provides second order accuracy, independent of the perturbation parameter. Numerical results are presented to illustrate the efficiency of the method.

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Aziz, T., Khan, A.: A spline method for second-order singularly perturbed boundary-value problems. J. Comput. Appl. Math. 147(2), 445–452 (2002)MathSciNetCrossRefMATH

Bestehorn, M., Grigorieva, E.V.: Formation and propagation of localized states in extended systems. Annalen der Physik 13(78), 423–431 (2004)MathSciNetCrossRefMATH

Doolan, E.P., Miller, J.J., Schilders, W.H.: Uniform Numerical Methods for Problems with Initial and Boundary Layers. Boole Press, Dublin (1980)MATH

Elsgolts, L.E., El-Sgol-Ts, L.E., El-Sgol-C, L.E.: Qualitative methods in mathematical analysis. American Mathematical Society, Providence (1964)

Geng, F.Z., Qian, S.P., Cui, M.G.: Improved reproducing kernel method for singularly perturbed differential–difference equations with boundary layer behavior. Appl. Math. Comput. 252, 58–63 (2015)MathSciNetMATH

Kadalbajoo, M.K., Kumar, D.: Fitted mesh B-spline collocation method for singularly perturbed differential–difference equations with small delay. Appl. Math. Comput. 204(1), 90–98 (2008)MathSciNetMATH

Kadalbajoo, M.K., Ramesh, V.P.: Hybrid method for numerical solution of singularly perturbed delay differential equations. Appl. Math. Comput. 187(2), 797–814 (2007)MathSciNetMATH

Kadalbajoo, M.K., Sharma, K.K.: An \(\varepsilon \)-uniform fitted operator method for solving boundary-value problems for singularly perturbed delay differential equations: layer behavior. Int. J. Comput. Math. 80(10), 1261–1276 (2003)MathSciNetCrossRefMATH

Kadalbajoo, M.K., Sharma, K.K.: Numerical analysis of singularly perturbed delay differential equations with layer behavior. Appl. Math. Comput. 157(1), 11–28 (2004)MathSciNetMATH

10.

Kadalbajoo, M.K., Sharma, K.K.: \(\varepsilon \)-Uniform fitted mesh method for singularly perturbed differential–difference equations: Mixed type of shifts with layer behavior. Int. J. Comput. Math. 81(1), 49–62 (2004)MathSciNetCrossRefMATH

11.

Kadalbajoo, M.K., Sharma, K.K.: A numerical method based on finite difference for boundary value problems for singularly perturbed delay differential equations. Appl. Math. Comput. 197(2), 692–707 (2008)MathSciNetMATH

12.

Lange, C.G., Miura, R.M.: Singular perturbation analysis of boundary value problems for differential–difference equations. V. small shifts with layer behavior. SIAM J. Appl. Math. 54(1), 249–272 (1994)MathSciNetCrossRefMATH

13.

Lange, C.G., Miura, R.M.: Singular perturbation analysis of boundary value problems for differential–difference equations. SIAM J. Appl. Math. 42(3), 502–531 (1982)MathSciNetCrossRefMATH

14.

Lange, C.G., Miura, R.M.: Singular perturbation analysis of boundary value problems for differential–difference equations. IV. A nonlinear example with layer behavior. Stud. Appl. Math. 84(3), 231–273 (1991)MathSciNetCrossRefMATH

15.

Lange, C.G., Miura, R.M.: Singular perturbation analysis of boundary-value problems for differential–difference equations. VI. small shifts with rapid oscillations. SIAM J. Appl. Math. 54(1), 273–283 (1994)MathSciNetCrossRefMATH

16.

Lasota, A., Wazewska, M.: Mathematical models of the red blood cell system. Mat. Stos 6, 25–40 (1976)

17.

Liu, L.B., Chen, Y.: Maximum norm a posteriori error estimates for a singularly perturbed differential difference equation with small delay. Appl. Math. Comput. 227, 801–810 (2014)MathSciNetMATH

18.

Mackey, M.C., Glass, L.: Oscillation and chaos in physiological control systems. Science 197(4300), 287–289 (1977)CrossRef

19.

O’malley, R.E.: Introduction to Singular Perturbations. Academic Press, New York (1974)MATH

20.

Patidar, K.C., Sharma, K.K.: \(\varepsilon \)-uniformly convergent non-standard finite difference methods for singularly perturbed differential difference equations with small delay. Appl. Math. Comput. 175(1), 864–890 (2006)MathSciNetMATH

21.

Ramos, J.I.: Exponential methods for singularly perturbed ordinary differential–difference equations. Appl. Math. Comput. 182(2), 1528–1541 (2006)MathSciNetMATH

22.

Varga, R.S.: Matrix Iterative Analysis. Prentice Hall, Englewood Cliffs (1962)

23.

Young, D.M.: Iterative Solution of Large Systems. Academic Press, New York (1971)MATH

Titel: A numerical approach for solving singularly perturbed convection delay problems via exponentially fitted spline method
verfasst von: Ravi Kanth Adivi Sri Venkata
Murali Mohan Kumar Palli
Publikationsdatum: 01.09.2017
Verlag: Springer Milan
Erschienen in: Calcolo / Ausgabe 3/2017
Print ISSN: 0008-0624
Elektronische ISSN: 1126-5434
DOI: https://doi.org/10.1007/s10092-017-0215-6

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