Differential quadrature solutions of the generalized burgers-fisher equation with a strong stability preserving high-order time integration

Mathematical and Computational Applications

Volumn 16, Issue 2, 2011, Pages 477-486

  Sari, Murat ^a  

^a PAMUKKALE UNIVERSITY   (Turkey)

Author keywords

Differential Quadrature Method; Generalized Burgers Fisher Equation; Nonlinear PDE; Strong Stability Preserving Runge Kutta

Indexed keywords

DIFFERENTIATION (CALCULUS); NONLINEAR EQUATIONS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS;

APPROXIMATE SOLUTION; BURGERS-FISHER EQUATION; DIFFERENTIAL QUADRATURE; DIFFERENTIAL QUADRATURE METHODS; HIGH ORDER TIME INTEGRATIONS; NON LINEAR PDE; NUMERICAL APPROXIMATIONS; STRONG STABILITY PRESERVING;

RUNGE KUTTA METHODS;

EID: 79952980071     PISSN: 1300686X     EISSN: None     Source Type: Journal    
DOI: 10.3390/mca16020477     Document Type: Article

References (33)

1. R.A. Fisher, The wave of advance of advantageous genes, Annals of Eugenics, 7, 355-369, 1937.
2. D. Kaya and S.M. El-Sayed, A numerical simulation and explicit solutions of the generalized Burger- Fisher equation, Applied Mathematics and Computation, 152, 403413, 2004.
3. H.N.A. Ismail and A.A.A. Rabboh, A restrictive Padé approximation for the solution of the generalized Fisher and Burger-Fisher equation, Applied Mathematics and Computation, 154, 203-210, 2004.
4. H.N.A. Ismail, K. Raslan and A.A.A. Rabboh, Adomian decomposition method for Burger's Huxley and Burger's-Fisher equations, Applied Mathematics and Computation, 159, 291-301, 2004.
5. H. Chen and H. Zhang, New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation, Chaos, Solitons and Fractals 19, 71-76, 2004.
6. S.A. El-Wakil and M.A. Abdou, Modified extended tanh-function method for solving nonlinear partial differential equation, Chaos, Solitons and Fractals, 31,1256-1264, 2007. (Pubitemid 44349165)
7. A.M. Wazwaz, The tanh method for generalized forms of nonlinear heat conduction and Burgers-Fisher equations, Applied Mathematics and Computation, 169, 321-338, 2005.
8. A.M. Wazwaz, The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations, Applied Mathematics and Computation, 188, 1467-1475, 2007.
9. M. Moghimi and F.S.A. Hejazi, Variational iteration method for solving generalized Burger-Fisher and Burger equations, Chaos, Solitons and Fractals, 33, 1756-1761, 2007. (Pubitemid 46413057)
10. H. Fahmy, Travelling wave solutions for some time-delayed equations through factorizations, Chaos, Solitons and Fractals, 38,1209-1216, 2008.
11. A. Golbabai and M. Javidi, A spectral domain decomposition approach for the generalized Burger's-Fisher equation, Chaos, Solitons and Fractals, 39, 385-392, 2009.
12. R. Bellman, B.G. Kashef and J. Casti, Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations, Journal of Computational Physics, 10, 40-52, 1972.
13. C.W. Bert and M. Malik, Differential quadrature method in computational mechanics: A review, Applied Mechanics Review, 49, 1-27, 1996. (Pubitemid 126614778)
14. O. Civalek, Large Deflection Static and Dynamic Analysis of Thin Circular Plates Resting on Two-Parameter Elastic Foundation: HDQ/FD Coupled Methodology Approaches, International Journal of Computational Mechanics, 2(2), 271-291, 2005.
15. B. Kaya, Solution of the advection-diffusion equation using the differential quadrature method, KSCE Journal of Civil Engineering, 14(1), 69-75, 2010.
16. B. Kaya, Y. Arisoy, Differential Quadrature Method for Linear Long Wave Propagation in Open Channels, 'Wave Propagation in Materials for Modern Applications', Ed.; Andrey Petrin, ISBN 978-953-7619-65-7, Published by Intech, Vukovar, Croatia, 253-266, 2010.
17. M. Sari, Differential quadrature method for singularly perturbed two-point boundary value problems, Journal of Applied Sciences 8, 1091-1096, 2008.
18. C. Shu, Generalized differential-integral quadrature and application to the simulation of incompressible viscous flows including parallel computation, Ph.D. Thesis, University of Glasgow, UK, 1991.
19. C. Shu and B.E. Richards, Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations, International Journal for Numerical Methods in Fluids 15(7), 791-798, 1992. (Pubitemid 23557497)
20. U. Yücel, Approximations of Sturm-Liouville eigenvalues using differential quadrature (DQ) method, Journal of Computational and Applied Mathematics, 192, 310-319, 2006.
21. U. Yücel and M. Sari, Differential quadrature method (DQM) for a class of singular two-point boundary value problems, International Journal of Computer Mathematics, 86, 465-475, 2009.
22. Z. Zong and KY. Lam, A localized differential quadrature (LDQ) method and its applications to the 2D wave equation, Computational Mechanics, 29, 382-391, 2002. (Pubitemid 35422278)
23. M. Sari and G. Gürarslan, Numerical solutions of the generalized Burgers-Huxley equation by a differential quadrature method, Mathematical Problems in Engineering, 2009, 2009, Article ID 370765.
24. G. Gürarslan and M. Sari, Numerical solutions of linear and nonlinear diffusion equations by a differential quadrature method (DQM), Communications in Numerical Methods in Engineering (2009) DOI: 10.1002/cnm.1292
25. S.T. Choi and Y.T. Chou, Structural analysis by differential quadrature method using the modified weighting matrices, Proceedings of American Society of Mechanical Engineers International Computer in Engineering Conference, Atlanta, Georgia, U.S.A., 1998.
26. K.M. Liew, Y.Q. Huang and J.N. Reddy, Analysis of general shaped thin plates by the moving least-squares differential quadrature method, Finite Elements in Analysis and Design, 40, 1453-1474, 2004.
27. F.L. Liu and K.M. Liew, Differential quadrature element method: a new approach for free vibration analysis of polar Mindlin plates having discontinuities, Computer Methods in Applied Mechanics and Engineering,179, 407-423, 1999. (Pubitemid 30504374)
28. A.G. Striz, W.L. Chen and C.W. Bert, Static analysis of structures by quadratic element method (QEM), International Journal of Solids and Structures, 31, 2807-2818, 1994.
29. H. Zhong, Triangular differential quadrature and its application to elastostatic analysis of Reissner plates, International Journal of Solids and Structures, 38, 2821-2832, 2001. (Pubitemid 32257396)
30. C. Shu and Y.T. Chew, Fourier expansion-based differential quadrature and its application to Helmholtz eigenvalue problems, Communications in Numerical Methods in Engineering, 13, 643-653, 1997. (Pubitemid 127548006)
31. C. Shu and H. Xue, Explicit computation of weighting coefficients in the harmonic differential quadrature, Journal of Sound and Vibration, 204, 549-555, 1997. (Pubitemid 127401724)
32. C. Shu, Differential Quadrature and Its Application in Engineering, Springer Verlag, London, 2000.
33. S. Gottlieb, C.-W Shu, E. Tadmor, Strong stability-preserving high-order time discretization methods, SIAM Review 43, 89-112, 2001. (Pubitemid 32406893)