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Numerical solution of singularly perturbed two parameter problems using exponential splines

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we have studied a method based on exponential splines for numerical solution of singularly perturbed two parameter boundary value problems. The boundary value problem is solved on a Shishkin mesh by using exponential splines. Numerical results are tabulated for different values of the perturbation parameters. From the numerical results, it is found that the method approximates the exact solution very well.
Rocznik
Strony
160--172
Opis fizyczny
Bibliogr. 29 poz., tab., wykr.
Twórcy
autor
  • Department of Mathematics, Prasad V Potluri Siddhartha Institute of Technology Vijayawada-520007, Andhra Pradesh, INDIA
autor
  • Department of Mathematics, Vallurupalli Nageswara Rao Vignana Jyothi Institute of Engineering and Technology (VNR VJIET) Bachupaly, Hyderabad-500090, INDIA
  • Department of Aeronautics and Astronautics, Air Force Institute of Technology Wright Patterson Air Force Base Dayton, Ohio 45433, USA
autor
  • Department of Mathematics, Vallurupalli Nageswara Rao Vignana Jyothi Institute of Engineering and Technology (VNR VJIET) Bachupaly, Hyderabad-500090, INDIA
Bibliografia
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  • [3] Ewing R.E. ( 1983) : The Mathematics of Reservoir Simulation.– SIAM, Philadelphia.
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  • [6] Markowich P.A., Ringhofer C.A., Selberherr S. and Lentini M. (1983): A singular perturbation approach for the analysis of the fundamental semiconductor equations.– IEEE Trans. Electron Device, vol.30, pp.1165-1180.
  • [7] Van Roosbroeck W.V. (1950): Theory of flows of electrons and holes in germanium and other semiconductors.– Bell Syst. Tech. J., vol 29, pp.560-607.
  • [8] Murray J.D. (1977): Lectures on Nonlinear Differential Equation Models in Biology.– Clarendon Press, Oxford.
  • [9] Weekman V.W. and Gorring R.L. (1965): Influence of volume change on gas-phase reactions in porous catalysts.– J. Catalysis, vol.4, pp.260-270.
  • [10] Gilberg D. and Trudinger N. (1977): Elliptic Partial Differential Equations of Second Order.– Springer-Verlag, p.518.
  • [11] Allen D. N. and de G.Southwell R.V. (1955): Relaxation methods applied to determine the motion in two dimensions of a viscous fluid past a fixed cylinder.– Quart. J.Mech. Appl. Math., vol.8, pp.129-145.
  • [12] Il’in A.M. (1969): A difference scheme for a differential equation with a small parameter multiplying the highest derivative (in Russian).– Mat. Zametki, vol.6, pp. 237-248, English translation: Math. Notes., vol.6, No.2, pp.596-602.
  • [13] Kellogg R. B. and Tsan A.(1978): Analysis of some difference approximations for a singular perturbation problem without turning points.– Math. Comp., vol.32, No.144, pp.1025-1039.
  • [14] El-Mistikawy T.M. and Werle M.J. (1978): Numerical method for boundary layers with blowing – the exponential box scheme.– AIAA J., vol.16, pp.749-751.
  • [15] Berger A.E., Soloman J.M. and Ciment M. (1981): An analysis of a uniformly accurate difference method for a singular perturbation problem.– Math. Comp., vol.37, No.155, pp.79-94.
  • [16] Hegarty A.F., Miller J.J.H. and O’Riordan E. (1980): Uniform second order difference schemes for singular perturbation problems. Boundary and interior layers computational and asymptotic methods.– Proc. Conf., Trinity College, Dublin, pp.301-305.
  • [17] Roos H.G. (1994): Ten ways to generate the Il’in and related schemes.– J. Comput. Appl. Math., vol.53, No.1, pp.4359.
  • [18] Bakhvalov N.S. (1969): On the optimization of the methods for solving boundary value problems in the presence of a boundary layer (in Russian).– Z. Vycisl. Mat i Mat. Fiz., vol.9, pp.841-859.
  • [19] Vulanovic R., Herceg D. and Petrovic N. (1986): On the extrapolation for a singularly perturbed boundary value problem.– Computing, vol.36, pp.69-79.
  • [20] Gartland E.C. (1988): Graded-mesh difference schemes for singularly perturbed two-point boundary value problems.– Math. Comput., vol.51, No.184, pp.631-657.
  • [21] Shishkin G.I. (1989): Approximation of solutions of singularly perturbed boundary value problems with a parabolic boundary layer.– U.S.S.R. Comput. Math. and Math. Phys., vol.29, No.4, pp.1-10.
  • [22] Miller J.J.H., O’Riordan E. and Shishkin G.I. (1996): Fitted Numerical Methods for Singular Perturbation Problems. Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions.– World Scientific, Singapore, p.192.
  • [23] O’Malley Jr. R.E. (1967): Singular perturbations of boundary value problems for linear ordinary differential equations involving two-parameters.– J. Math. Anal. Appl., vol.19, pp.291-308.
  • [24] Vulanovic R. and Ohio C. (2001): A higher order scheme for quasilinear boundary value problems with two small parameters.– Computing, vol.67, pp.287-303.
  • [25] Roos H.G. and Uzela Z. (2003): The SDFEM for a convection-diffusion problem with two small parameter.– Comput. Methods Appl. Math., vol.3, pp.443-458.
  • [26] Linss T. (2010): A posterior error estimation for a singularly perturbed problem with two small parameters.– Int. J. Numer. Anal. Model., vol.7, pp.491-506.
  • [27] Zahra W.K. and Ashraf M. EI Mhlawy (2013): Numerical solution of two-parameter singularly perturbed boundary value problems via exponential spline.– King Saud University, vol.25, pp.201-208.
  • [28] Linss T. and Roos H-G. (2004): Analysis of a finite-difference scheme for a singularly perturbed problem with two small parameters.– J.Math.Anal.Apppl., vol.289, pp.424-442.
  • [29] Kadalbajoo M.K. and Yadaw A.S. (2008): B-spline collection method for a two-parameter singularly perturbed convection-diffusion boundary value problem.– Appl. Math. Comput., vol.201, pp.504-513.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c4ac0da9-09b6-4524-a7b0-4d81329c0acc
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