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

Year 2018, Volume: 6 Issue: 1, 45 - 54, 30.04.2018

Bahar Karaman Yılmaz Dereli

https://doi.org/10.20290/aubtdb.304095
Cited By: 1

Abstract

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.

Keywords

Radial Basis Functions General Rosenau KdV-RLW equation

References

  • [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.

Year 2018, Volume: 6 Issue: 1, 45 - 54, 30.04.2018

Bahar Karaman Yılmaz Dereli

https://doi.org/10.20290/aubtdb.304095
Cited By: 1

Abstract

References

  • [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.
There are 10 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Bahar Karaman

Yılmaz Dereli

Publication Date April 30, 2018
Published in Issue Year 2018 Volume: 6 Issue: 1

Cite

APA Karaman, B., & Dereli, Y. (2018). MESHLESS METHOD BASED ON RADIAL BASIS FUNCTIONS FOR GENERAL ROSENAU KdV-RLW EQUATION. Anadolu University Journal of Science and Technology B - Theoretical Sciences, 6(1), 45-54. https://doi.org/10.20290/aubtdb.304095
AMA Karaman B, Dereli Y. MESHLESS METHOD BASED ON RADIAL BASIS FUNCTIONS FOR GENERAL ROSENAU KdV-RLW EQUATION. AUBTD-B. April 2018;6(1):45-54. doi:10.20290/aubtdb.304095
Chicago Karaman, Bahar, and Yılmaz Dereli. “MESHLESS METHOD BASED ON RADIAL BASIS FUNCTIONS FOR GENERAL ROSENAU KdV-RLW EQUATION”. Anadolu University Journal of Science and Technology B - Theoretical Sciences 6, no. 1 (April 2018): 45-54. https://doi.org/10.20290/aubtdb.304095.
EndNote Karaman B, Dereli Y (April 1, 2018) MESHLESS METHOD BASED ON RADIAL BASIS FUNCTIONS FOR GENERAL ROSENAU KdV-RLW EQUATION. Anadolu University Journal of Science and Technology B - Theoretical Sciences 6 1 45–54.
IEEE B. Karaman and Y. Dereli, “MESHLESS METHOD BASED ON RADIAL BASIS FUNCTIONS FOR GENERAL ROSENAU KdV-RLW EQUATION”, AUBTD-B, vol. 6, no. 1, pp. 45–54, 2018, doi: 10.20290/aubtdb.304095.
ISNAD Karaman, Bahar - Dereli, Yılmaz. “MESHLESS METHOD BASED ON RADIAL BASIS FUNCTIONS FOR GENERAL ROSENAU KdV-RLW EQUATION”. Anadolu University Journal of Science and Technology B - Theoretical Sciences 6/1 (April 2018), 45-54. https://doi.org/10.20290/aubtdb.304095.
JAMA Karaman B, Dereli Y. MESHLESS METHOD BASED ON RADIAL BASIS FUNCTIONS FOR GENERAL ROSENAU KdV-RLW EQUATION. AUBTD-B. 2018;6:45–54.
MLA Karaman, Bahar and Yılmaz Dereli. “MESHLESS METHOD BASED ON RADIAL BASIS FUNCTIONS FOR GENERAL ROSENAU KdV-RLW EQUATION”. Anadolu University Journal of Science and Technology B - Theoretical Sciences, vol. 6, no. 1, 2018, pp. 45-54, doi:10.20290/aubtdb.304095.
Vancouver Karaman B, Dereli Y. MESHLESS METHOD BASED ON RADIAL BASIS FUNCTIONS FOR GENERAL ROSENAU KdV-RLW EQUATION. AUBTD-B. 2018;6(1):45-54.

Cited By

Solving the Generalized Rosenau-KdV Equation by the Meshless Kernel-Based Method of Lines
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