A numerical meshfree technique for the solution of the MEW equation

CMES - Computer Modeling in Engineering and Sciences

Volumn 38, Issue 1, 2008, Pages 1-23

  Haq, Sirajul ^a   Islam, Sirajul ^b   Ali, Arshed ^a  

^a GIK INSTITUTE OF ENGINEERING SCIENCES AND TECHNOLOGY   (Pakistan)

^b UNIVERSITY OF ENGINEERING AND TECHNOLOGY   (Pakistan)

Author keywords

Generalized equal width wave (GEW) equation; Modified equal width wave (MEW) equation; Radial basis functions (RBFs); Solitary wave; Stability analysis

Indexed keywords

LIQUID WAVES; RADIAL BASIS FUNCTION NETWORKS;

GENERALIZED EQUAL WIDTH WAVE (GEW) EQUATION; MODIFIED EQUAL WIDTH WAVE (MEW) EQUATION; RADIAL BASIS FUNCTIONS (RBFS); SOLITARY WAVE; STABILITY ANALYSIS;

WAVES;

EID: 62449303553     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

1. Abdulloev, Kh. O.; Bogolubsky, I. L.; Makhankov, V. G. (1976): One more example of inelastic soliton interaction. Physics Letter, vol. 56A, pp. 427-428.
2. Atluri, S. N.; Han, Z. D.; Rajendran, A. M. (2004): A New Implementation of the Meshless Finite Volume Method, Through the MLPG "Mixed" Approach. CMES: Computer Modeling in Engineering & Sciences, vol. 6(6), pp. 491-514.
3. Chantasiriwan, S. (2006): Performance of Multiquadric Collocation Method in Solving Lid-driven Cavity Flow Problem with Low Reynolds Number. CMES: Computer Modeling in Engineering & Sciences, vol. 15(3), pp. 137-146.
4. Cheng, A. H. D.; Golberg, M. A.; Kansa, E. J.; Zammito, G. (2003): Exponential convergence and H - c multiquadric collocation method for partial differential equations. Numer Methods for Partial Diff Eq, vol. 19, pp. 571-594.
5. Esen, A. (2006): A lumped Galerkin method for the numerical solution of the modified equal-width wave equation using quadratic B-splines. Int J Comput Math, vol. 83(5-6), pp. 449-459.
6. Esen, A.; Kutluay, S. (2008): Solitary wave solutions of the modified equal width wave equation. Comm Nonlinear Science and Numer Simul, vol. 13, pp. 1538-1546.
7. Evans, D. J.; Raslan, K. R. (2005): Solitary waves for the generalized equal width (GEW) equation. Int J Comp Math, vol. 82(4), 445-55.
8. Fasshauer, G. E. (1996): Solving partial differential equations by collocation with radial basis functions. In: A. L. Me'chaute'(ed.) Proceedings of Chamonix, Vanderbilt University Press, Nashville, TN, pp. 1-8.
9. Franke, C.; Schaback, R. (1998): Solving partial differential equations by collocation with radial basis functions. Appl Math Comput, vol. 93, pp. 73-82.
10. Franke, A.; Schaback, R. (1998): Convergence order estimates of meshless collocation methods using radial basis functions. Adv Comput Math, vol. 8, pp. 381-399.
11. Hamdi, S.; Enright, W. H.; Schiesser, W. E.; Gottlieb J.J. (2003): Exact solutions of the generalized equal width wave equation. ICCSA, vol. 2, pp. 725-734.
12. Hon, Y. C.; Cheung, K. F.; Mao, X. Z.; Kansa, E. J. (1999): Multiquadric solution for shallow water equations. ASCE J Hydraulic Eng, vol. 125(5), pp. 524-533.
13. Hon, Y. C.; Mao, X. Z. (1998): An efficient numerical scheme for Burgers' equation. Appl Math Comput, vol. 95(1), pp.37-50.
14. Hon, Y.C.; Schaback, R. (2001): On unsymmetric collocation by radial basis functions. Appl Math Comput, vol. 119 , pp. 177-186.
15. Kansa, E. J. (1990): Multiquadrics scattered data approximation scheme with applications to Computational fluid-dynamics I, surface approximations and partial derivative estimates. Comput Math Appl, vol.19, pp. 127-145.
16. Khattak, A. J.; Siraj-ul-Islam (2008): A comparative numerical solutions of a class of KdV equations. Appl Math Comput, vol. 199, pp. 425-434.
17. Kosec, G.; Sarler, B. (2008): Local Collocation Method for Darcy Flow. CMES: Computer Modeling in Engineering & Sciences, vol. 25(3), pp. 197-207.
18. Li, J.; Chen, Y.; Pepper, D. (2003): Radial basis function method for 1-D and 2-D groundwater contaminant transport modeling. Comput Mech, vol. 32, pp. 10-15.
19. Lorentz, R. A.; Narcowich, F. J.;Ward, J. D. (2003): Collocation discretizations of the transport equation with radial basis functions. Appl Math Comput, vol.145, pp. 97-116.
20. Lu, J. (2007): He's variational iteration method for the modified equal width equation. Chaos, Solitons and Fractals, In press.
21. Morrison, P. J.; Meiss, J. D.; Carey, J. R. (1984): Scattering of RLW solitary waves. Physica D, vol. 11, pp. 324-336.
22. Peregrine, A. H. (1966): Calculations of the development of an undular bore. J Fluid Mech, vol. 25(2), pp. 321-330.
23. Rubin, S. G.; Graves, R. A. (1975): Cubic spline approximation for problems in fluid mechanics. NASA TR R-436, Washington, DC.
24. Saka, B. (2007): Algorithms for numerical solution of the modified equal width wave equation using collocation method. Math Comp Modl, vol. 45, pp. 1096-1117.
25. Siraj-ul-Islam; Sirajul Haq; Arshed Ali (2008): A meshfree method for the numerical solution of RLW equation, J. Comp. Appl. Math, DOI: 10.1016.
26. Siraj-ul-Islam; Sirajul Haq; Marjan Uddin (2008): A meshfree interpolation method for the numerical solution of the coupled nonlinear partial differential equations. Eng Anal Bound Elem, In Press.
27. Wazwaz, A. M. (2006): The tanh and sine-cosine methods for a reliable treatment of the modified equal width equation and its variants. Comm Nonlinear Sci Numer Simul, vol. 11, pp. 148-160.
28. Wu, Z.; Hon, Y. C. (2003): Convergence error estimates in solving free boundary diffusion problem by radial basis functions method. Eng Anal Bound Elem, vol. 27, pp. 73-79.
29. Zaki, S. I. (2000): Solitary wave interactions for the modified equal width equation. Comput Phys Comm, vol.126, pp. 219-231.