An extended finite difference method for singular perturbation problems on a non-uniform mesh

• Autorzy: Swarnakar D. , Kumar V. Ganesh , Soujanya G. B. S. L.

Identyfikatory

DOI

10.2478/ijame-2022-0013

• Języki publikacji: EN

Abstrakty

EN

An extended second order finite difference method on a variable mesh is proposed for the solution of a singularly perturbed boundary value problem. A discrete equation is achieved on the non uniform mesh by extending the first and second order derivatives to the higher order finite differences. This equation is solved efficiently using a tridiagonal solver. The proposed method is analysed for convergence, and second order convergence is derived. Model examples are solved by the proposed scheme and compared with available methods in the literature to uphold the method.

Słowa kluczowe

EN

non uniform grid; finite difference method; singular perturbation; boundary layer

PL

siatka niejednorodna; metoda różnic skończonych; warstwa graniczna

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2022
• Tom: Vol. 27, no. 1
• Strony: 203--214
• Opis fizyczny: Bibliogr. 15 poz., tab., wykr.

Twórcy

autor

Swarnakar D.

• Department of Mathematics, VNR Vignana Jyothi Institute of Engineering and Technology Hyderabad, Telangana, INDIA

autor

Kumar V. Ganesh

• Department of Mathematics, VNR Vignana Jyothi Institute of Engineering and Technology Hyderabad, Telangana, INDIA

autor

Soujanya G. B. S. L.

• Department of Mathematics, University College for Women, Kakatiya University Warangal, Telangana, INDIA

Bibliografia

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• [9] Kadalbajoo M.K., Sharma K.K. (2008): A numerical method based on the finite difference for boundary value problems for singularly perturbed delay differential equations.– Mathematics and Computers in Simulation, vol.197, pp.692-707.
• [10] Hemker P.W. and Miller J.J.H. (1979): Numerical Analysis of Singular Perturbation Problem.– Academic Press, New York.
• [11] Kadalbajoo M.K. and Patidar K.C. (2003): Spline approximation method for solving self-adjoint singular perturbation problems on non-uniform grids.– J. Comput. Anal. Appl., vol.5, pp.425-451.
• [12] O'Malley R.E. (1974): Introduction to Singular Perturbations.– Academic Press, New York.
• [13] Miller J.J.H., O’Riordan E. and Shishkin G.I. (1996): Fitted Numerical Methods for Singular Perturbation Problems.– World Scientific, Singapore.
• [14] Aziz T. and Khan A. (2002): A spline method for second order singularly perturbed boundary-value problems.– J. Comput. Appl. Math., vol.147, pp.445-452.
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Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)