International Journal of Mathematics and Computational Science
Articles Information
International Journal of Mathematics and Computational Science, Vol.1, No.5, Oct. 2015, Pub. Date: Aug. 7, 2015
Comparison of Mesh-Based and Meshless Methods for Solving the Mathematical Model Arising of Launching Devices During the Firing
Pages: 317-323 Views: 1320 Downloads: 423
Authors
[01] S. Sarabadan, Departeman of Mathematics, Imam Hossein University, Tehran, Iran.
[02] M. Kafili, Departeman of Mathematics, Imam Hossein University, Tehran, Iran.
Abstract
In this paper, we apply different mesh-based and meshless methods for solving matrix system carried out from modelling the rockets stability during the firing. Sloped rocket launch and its stability during the firing is one of the most important kinds of defense instruments. The rockets stability during the firing path especially when they are unguided is very important for firing precision. Two mesh-based schemes as finite difference and B-spline methods and two meshless schemes as radial basis function (RBF) and radial basis functions based on finite difference (RBF-FD) are employed for solving underlying system. Numerical results are presented as tabular forms. They show that computational errors and CPU time for RBF-FD as a meshless method are better than other methods.
Keywords
Mesh-Based Method, Meshless Method, Sloped Rocket Launch
References
[01] H. Wendland, Scattered Data Approximation, Cambridge University Press, (2005).
[02] ‎M. D. Buhmann,Radial Basis Functions: Theory and Implementation, University of Gissen, Cambridge University Press, (2004).
[03] P. Somoiag, C. Moldoveanu, Numerical research on the stability of launching devices during firing, Defence Technology 9, (2013), 242-248.
[04] P. Somoiag, F. Moraru, D. Safta, C. Moldoveanu, A mathematical model for the motion of a rocket-launching device system on a heavy vehicle, Military technical academy, Romania, (2012).
[05] R. J. Leveque, Finite difference methods for differential equations, University of Washington, (2005).
[06] ‎R. Schaback, Improved error bounds for scattered data interpolation by radial basis functions, Math Comput, 68, (1999), 201-206.
[07] R. L. Hardy, Multiquadric equations of topography and other irregular surfaces, J Geophys Res, 76, (1971), 1905-1915.
[08] R. Franke, Scattered data interpolation: tests of some methods, Math Comput, 38, (1982), 181-200.
[09] ‎C. S. Huang, C. F. Lee, A. D. Cheng, Error estimate, optimal shape factor, and high precision computation of multiquadric collocation method, Eng Anal Bound Elem, 31, (2007), 614-623.
[10] ‎R. E. Carlson, T. A. Foley, The parameter R^2 in multiquadric interpolation, Comput Math Appl, 21, (1991), 29-42.
[11] ‎E. J. Kansa, R. E. Carlson, Improved accuracy of multiquadric interpolation using variable shape parameters, Comput Math Appl, 24, (1992), 99-120.
[12] ‎E. J. Kansa, R. C. Aldredge, L. Ling. Numerical simulation of two-dimensional combustion using mesh-free methods, Eng Anal Bound Elem, 33, (2009), 940-950.
[13] ‎S. A. Sarra, D. Sturgill, A random variable shape parameter strategy for radial basis function approximation methods, Eng Anal Bound Elem, 33, (2009), 1239-1245.
[14] V. Bayona, M. Moscoso, M. Carretero, M. Kindelan, RBF-FD formulas and convergence properties, Journal of computational physics, 229, (2010), 8281-8295.
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