MESHLESS METHOD BASED ON RADIAL BASIS FUNCTIONS FOR GENERAL ROSENAU KdV-RLW EQUATION

Yıl 2018, Cilt: 6 Sayı: 1, 45 - 54, 30.04.2018

Bahar Karaman , Yılmaz Dereli

https://doi.org/10.20290/aubtdb.304095

Cited By: 1

Öz

In
the present study, the meshless method based on radial basis functions is
applied for finding the numerical solution of the general Rosenau KdV-RLW
equation. Firstly, Crank-Nicolson and forward finite difference methods are
used for discretization of the unknown function  and its time derivative,
respectively. A linearization technique is applied for the approximate solution
of the equation. Secondly, we calculate the numerical values of invariants of
the motions to examine the fundamental conservative properties of the equation.
Also, the error norms are computed to determine the accuracy of the proposed
method. Linear stability analysis is tested to determine whether the present
method is stable or unstable. The scheme gives unconditionally stable. At the
end of this paper, obtained results indicate the accuracy and applicability of
this method.

Anahtar Kelimeler

Radial Basis Functions, General Rosenau KdV-RLW equation

Kaynakça

• [1] Mittal R. C, Jain R. K. Numerical solution of general Rosenau-RLW equation using quantic B-splines collocation method. Communications in Numerical Analysis, 2012.
• [2] Zuo J. M, Zhang Y. M, Zhang T. D, Chang F. A new conservative difference scheme for the general Rosenau-RLW equation. Boundary Value Problems, 2010.
• [3] Wongsaijai B, Poochinapan K, Disyadej T. A compact finite difference method for solving the general Rosenau-RLW equation. IAENG International Journal of Applied Mathematics, 2014.
• [4] Pan X, Zhang L. Numerical simulation for general Rosenau-RLW equation: an averaged linearized conservative scheme. Mathematical Problems in Engineering, 2012.
• [5] Esfahani A. Solitary wave solutions for generalized Rosenau-KdV equation. Communications in Theoretical Physics, 2011; 55: 396-398.
• [6] Zheng M, Zhou J. An average linear difference scheme for the generalized Rosenau-KdV equation. Journal of Applied Mathematics, 2014.
• [7] Luo Y, Xu Y, Feng M. Conservative difference scheme for Generalized Rosenau-KdV equation. Advances in Mathematical Physics, 2014.
• [8] Kansa E. J. Multiquadrics - A scattered data approximation scheme with applications to computational fluid dynamics I. Computers and Mathematics with Applications 1990; 19: 127-145.
• [9] Kansa E. J. Multiquadrics - A scattered data approximation scheme with applications to computational fluid dynamics II. Computers and Mathematics with Applications 1990; 19: 147-161.
• [10] Franke C, Schaback R. Convergence order estimates of meshless collocation methods using radial basis functions. Advances in Computational Mathematics 1998; 8: 381-399.