과제정보
This work was supported by the Research Management Centre, Universiti Malaysia Sabah.
참고문헌
- A. R. Abdullah, The four point explicit decoupled group (EDG) Method: a fast Poisson solver, Int. J. Comput. Math., 38(1-2)(1991), 61-70. https://doi.org/10.1080/00207169108803958
- R. Abedian, H. Adibi and M. Dehghan, A high-order weighted essentially nonoscillatory (WENO) finite difference scheme for nonlinear degenerate parabolic equations, Comput. Phys. Commun., 184(8)(2013), 1874-1888. https://doi.org/10.1016/j.cpc.2013.03.012
- L. H. Ali, J. Sulaiman and S. R. M. Hashim, Numerical solution of fuzzy Fredholm integral equations of second kind using half-sweep Gauss-Seidel iteration, J. Eng. Sci. Technol., 15(5)(2020), 3303-3313.
- R. Borana, V. Pradhan and M. Mehta, Numerical solution of instability phenomenon arising in double phase flow through inclined homogeneous porous media, Perspect Sci., 8(2016), 225-227.
- J. V. L. Chew and J. Sulaiman, Application of MSOR iteration with Newton scheme for solutions of 1D nonlinear porous medium equations, AIP Conference Proceedings, (2016), article no. 20017. doi: 10.1063/1.4952497
- J. V. L. Chew and J. Sulaiman, Implicit solution of 1D nonlinear porous medium equation using the four-point Newton-EGMSOR iterative method, J. Appl. Comput. Mech., 15(2)(2016), 11-21. doi: 10.17512/jamcm.2016.2.02
- J. V. L. Chew and J. Sulaiman, Solution of one-dimensional porous medium equation using half-sweep Newton-MSOR iteration, Adv. Sci. Lett., 24(3)(2018), 1906-1911. https://doi.org/10.1166/asl.2018.11186
- C. H. Cho, On the finite difference approximation for blow-up solutions of the porous medium equation with a source, Appl. Numer. Math., 65(2013), 1-26. https://doi.org/10.1016/j.apnum.2012.11.001
- D. J. Evans, Group explicit iterative methods for solving large linear systems, Int. J. Comput. Math., 17(1)(1985), 81-108. https://doi.org/10.1080/00207168508803452
- D. R. Kincaid and D. M. Young, The modified successive overrelaxation method with fixed parameters, Math. Comp., 26(119)(1972), 705-717. https://doi.org/10.1090/S0025-5718-1972-0331746-2
- Y. Liu, C. W. Shu and M. Zhang, High order finite difference WENO schemes for nonlinear degenerate parabolic equations, SIAM J. Sci. Comput., 33(2)(2011), 939-965. https://doi.org/10.1137/100791002
- N. A. Mat Ali, R. Rahman, J. Sulaiman and K. Ghazali, Solutions of reactiondiffusion equations using similarity reduction and HSSOR iteration, Indones. J. Electr. Eng. Comput. Sci., 16(3)(2019), article no. 1430.
- L. Monsaingeon, An explicit finite-difference scheme for one-dimensional generalized porous medium equations: interface tracking and the hole filling problem, ESAIM Math. Model. Numer. Anal., 50(4)(2016), 1011-1033. https://doi.org/10.1051/m2an/2015063
- F. A. Muhiddin, J. Sulaiman and A. Sunarto, Grunwald implicit solution of one-dimensional time-fractional parabolic equations using HSKSOR iteration, J. Phys. Conf. Ser., 1489(2020), article no. 12025.
- A. D. Polyanin and V. F. Zaitsev, Handbook of nonlinear partial differential equations, Boca Raton: Chapman & Hall(2004).
- M. Safari, M. J. Ameri and A. Naderifar, An efficient boundary control for porous media equation: motivated by water coning problem, Can. J. Chem. Eng., 97(2019), 888-902. https://doi.org/10.1002/cjce.23323
- A. Saudi and J. Sulaiman, An efficient two-stage half-sweep modified arithmetic mean (HSMAM) method for the solution of 2D elliptic equation, Adv. Sci. Lett., 24(3)(2018), 1917-1921. https://doi.org/10.1166/asl.2018.11188
- A. Sunarto and J. Sulaiman, Performance numerical method half-sweep preconditioned Gauss-Seidel for solving fractional diffusion equation, Math. Model. Eng. Probl., 7(2)(2020), 201-204. https://doi.org/10.18280/mmep.070205
- R. S. Varga, Gersgorin and His Circles, Berlin: Springer(2004).
- J. L. Vazquez, The Porous Medium Equation, Oxford University Press(2006).
- A. M. Wazwaz, Exact solutions to nonlinear diffusion equations obtained by the decomposition method, Appl. Math. Comput., 123(1)(2001), 109-122. https://doi.org/10.1016/S0096-3003(00)00064-3