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Implicit solution of 1d nonlinear porous medium equation using the four-point Newton- EGMSOR iterative method

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Języki publikacji
EN
Abstrakty
EN
The numerical method can be a good choice in solving nonlinear partial differential equations (PDEs) due to the difficulty in finding the analytical solution. Porous medium equation (PME) is one of the nonlinear PDEs which exists in many realistic problems. This paper proposes a four-point Newton-EGMSOR (4-Newton-EGMSOR) iterative method in solving 1D nonlinear PMEs. The reliability of the 4-Newton-EGMSOR iterative method in computing approximate solutions for several selected PME problems is shown with comparison to 4-Newton-EGSOR, 4-Newton-EG and Newton-Gauss-Seidel methods. Numerical results showed that the proposed method is superior in terms of the number of iterations and computational time compared to the other three tested iterative methods.
Rocznik
Strony
11--21
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
  • Faculty of Science and Natural Resources, University Malaysia Sabah Sabah, Malaysia
autor
  • Faculty of Science and Natural Resources, University Malaysia Sabah Sabah, Malaysia
Bibliografia
  • [1] Mahmood T., Khan N., Thin film flow of a third grade fluid through porous medium over an inclined plane, International Journal of Nonlinear Science 2012, 14(1), 53-59.
  • [2] Khaled A.R.A., Vafai K., The role of porous media in modelling flow and heat transfer in biological tissues, International Journal of Heat and Mass Transfer 2003, 46, 4989-5003.
  • [3] Meher R., Mehta M.N., Meher S.K., Adomian decomposition method for dispersion phenomena arising in longitudinal dispersion of miscible fluid flow through porous media, Advances in Theoretical and Applied Mechanics 2010, 3(5), 211-220.
  • [4] Meher R.K., Meher S.K., Mehta M.N., A new approach to Backlund transformation for longitudinal dispersion of miscible fluid flow through porous media in oil reservoir during secondary recovery process, Theoretical and Applied Mechanics 2011, 38(1), 1-16.
  • [5] Meher R.K., Meher S.K., Analytical treatment and convergence of the Adomian decomposition method for instability phenomena arising during oil recovery process, International Journal of Engineering Mathematics 2013, Article ID-752561.
  • [6] Meher R.K., Meher S.K., Mehta M.N., Exponential self similar solutions technique for instability phenomenon arising in double phase flow through porous medium with capillary pressure, Applied Mathematics Sciences 2010, 4(27), 1329-1335.
  • [7] Pradhan V.H., Mehta M.N., Patel T., A numerical solution of nonlinear equation representing one-dimensional instability phenomena in porous media by finite element technique, International Journal of Advanced Engineering Technology 2011, 2(1), 221-227.
  • [8] Elsheikh A.M., Elzaki T.M., Variation iteration method for solving porous medium equation, International Journal of Development Research 2015, 5(6), 4677-4680.
  • [9] Wazwaz A.M., The variational iteration method: A powerful scheme for handling linear and nonlinear diffusion equations, Computers and Mathematics with Application 2007, 54, 933-939.
  • [10] Bhadane P.K.G., Pradhan V.H., Elzaki transform homotopy pertubation method for solving porous medium equation, International Journal of Research in Engineering and Technology 2013, 2(12), 116-119.
  • [11] Elzaki T.M., Hilal E.M.A., Homotopy perturbation and Elzaki transform for solving nonlinear partial differential equations, Mathematical Theory and Modeling 2012, 2(3), 33-42.
  • [12] Pamuk S., On the solution of the porous media equation by decomposition method: A review, Physics Letters A 2005, (344), 184-188.
  • [13] Sulaiman J., Hasan M.K., Othman M., Karim S.A.A., Newton-EGMSOR methods for solution of second order two-point nonlinear boundary value problems, Journal of Mathematics and System Science 2012, 2, 185-190.
  • [14] Saad Y., Iterative Methods for Sparse Linear Systems, 2nd ed., Society for Industrial and Applied Mathematics, Philadelphia 2003.
  • [15] Young D.M., Iterative methods for solving partial difference equations of elliptic type, Transactions of the American Mathematical Society 1954, 76, 92-111.
  • [16] Young D.M., Iterative Solution of Large Linear Systems, Academic Press, Florida 2014.
  • [17] Kincaid D.R., Young D.M., The modified successive over relaxation method with fixed parameters, Mathematics of Computation 1972, 26(119), 705-717.
  • [18] Evans D.J., Group explicit iterative methods for solving large linear systems, International Journal of Computer Mathematics 1985, 17, 81-108.
  • [19] Evans D.J., Abdullah A.R., A new explicit method for the diffusion-convection equation, Computers and Mathematics with Applications 1985, 11, 1-3.
  • [20] Polyanin A.D., Zaitsev V.F., Handbook of Nonlinear Partial Differential Equation, Chapman and Hall, Boca Raton 2004.
  • [21] Akhir M.K.M., Othman M., Sulaiman J., Majid Z.A., Suleiman M., Half-sweep modified successive over relaxation for solving two-dimensional Helmholtz equations, Australian Journal of Basic and Applied Sciences 2011, 5(12), 3033-3039.
  • [22] Othman M., Sulaiman J., Abdullah A.R., A parallel halfsweep multigrid algorithm on the shared memory multiprocessors, Malaysian Journal of Computer Science 2000, 13(2), 1-6.
  • [23] Muthuvalu M.S., Sulaiman J., Half-sweep geometric mean method for solution of linear Fredholm equations, Matematika 2008, 24(1), 75-84.
  • [24] Aruchunan E., Sulaiman J., Half-sweep conjugate gradient method for solving first order linear Fredholm integro-differential equations, Australian Journal of Basic and Applied Sciences 2011, 5, 38-43.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-da7da357-f06d-4948-8ee0-62d3171e80d2
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