NUMERICAL SOLUTION OF HIROTA-SATSUMA COUPLED KDV SYSTEM BY RBF-PS METHOD
Keywords:
Hirota-Satsuma Coupled KdV system; Radial basis functions; Pseudospectral method; Runge-Kutta 4th order method
Abstract
In this paper, the Hirota-Satsuma coupled Korteweg-de Vries system is solved numerically by using radialbasis function-Pseudospectral method. The radial basis functions are used to approximate the space derivatives in the system. Moreover, the system has become a system of ordinary differential equations with independent variable , and this system is solved by Runge-Kutta fourth order method, with the help of MATLAB R2020a. Also, a comparison has been made between approximate solutions obtained by the proposed method and exact solutions
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References
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Platte, R. B. and Driscoll, T. A. (2005). Polynomials and potential theory for Gaussian radial basis function interpolation. SIAM Journal on Numerical Analysis, 43(2), 750-766.
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Suarez, P. U. and Morales, J. H. (2014). Numerical solutions of two-way propagation of nonlinear
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Yao, G.; Siraj-ul-Islam and Sarler, B. (2012). Assessment of global and local meshless methods based on collocation with radial basis functions for parabolic partial differential equations in three dimensions. Engineering Analysis with Boundary Elements, 36(11), 1640-1648.
Yucel C.; Ali K. and Orkun T. (2017). On the New Solutions of the Conformable Time Fractional
Generalized Hirota-Satsuma Coupled KdV System. Seria Matematica – Informatica. Vol. 1. 37-49.
Burden, R. L. and Faires, J. D. (2011). Numerical Analysis. Ninth Edition. Brooks/Cole, Cengage
Learning.
Constantinides, A. and Mostoufi, N. (1999). Numerical Methods for Chemical Engineers with MATLAB Applications. Upper Saddle River, NJ: Prentice Hall PTR.
Eilbeck, J. C. and Manoranjan, V. S. (1986). A comparison of basis functions for the pseudo- spectral method for a model reaction-diffusion problem. Journal of Computational and Applied Mathematics, 15(3), 371-378.
Fan E. (2001). Soliton Solutions for a Generalized Hirota-Satsuma Coupled KdV Equation and a
Coupled MKdV Equation. Physics Letters A, Vol. 2852, No. 1-2, 18-22.
Fasshauer, G. E. (2007). Meshfree Approximation Methods with MATLAB. Interdisciplinary
Mathematical Sciences, Vol.6. World Scientific Publishing, Singapore.
Ferreira, A. J.; Kansa, E. J.; Fasshauer, G. E. and Leitao, V.M.A. (2009). Progress on Meshless Methods.
Springer Science and Business Media.
Fornberg, B. (1998). A Practical Guide to Pseudo- pectral Methods. Cambridge University Press.
Gao, Y.T.; Tian, B. (2021) Ion-acoustic shocks in space and laboratory dusty plasmas: Two-dimensional
and non-traveling-wave observable effects. Phys. Plasmas , 8, 3146.
Golub, G. H. and Ortega, J. M. (1992). Scientific Computing and Differential Equations: An
Introduction to Numerical Methods. Academic Press.
Haribaskaran, G. (2009). Numerical Methods. 2nd edition. University Science Press.
Jain, M. K. (1979). Numerical Solution of Differential Equations. John Wiley and Sons, New York.
Mahmoud A. E. Abdelrahman; M. B. Almatrafi and Abdulghani Alharbi (2020). Fundamental
Solutions for the Coupled KdV System and Its Stability. Symmetry. Vol. 12.
Manaa S.A., and Azzo Sh. M. (2022). Sumudu- Decomposition Method to Solve Generalized
Hirota-Satsuma Coupled Kdv System. Science Journal of University of Zakho. 10(2), 43-47.
Micchelli, C. A. (1986). Interpolation of scattered data: distances, matrices, and conditionally positive
definite functions. Const. Approx. 2, 11-22.
Platte, R. B. and Driscoll, T. A. (2005). Polynomials and potential theory for Gaussian radial basis function interpolation. SIAM Journal on Numerical Analysis, 43(2), 750-766.
Platte, R. B. and Driscoll, T. A. (2006). Eigenvalue stability of radial basis function discretizations for
time dependent problems. Computers and Mathematics with Applications, 51(8), 1251-1268.
Sarra, S. A. (2006). Integrated multiquadric radial basis function approximation methods. Computers and
Mathematics with Applications, 51(8), 1283-1296.
Suarez, P. U. and Morales, J. H. (2014). Numerical solutions of two-way propagation of nonlinear
dispersive waves using radial basis functions. International Journal of Partial Differential Equations, 2014, 1-8.
Trefethen, L. N. (2000). Spectral Methods in MATLAB. SIAM, Philadelphia.
Yao, G.; Siraj-ul-Islam and Sarler, B. (2012). Assessment of global and local meshless methods based on collocation with radial basis functions for parabolic partial differential equations in three dimensions. Engineering Analysis with Boundary Elements, 36(11), 1640-1648.
Yucel C.; Ali K. and Orkun T. (2017). On the New Solutions of the Conformable Time Fractional
Generalized Hirota-Satsuma Coupled KdV System. Seria Matematica – Informatica. Vol. 1. 37-49.
Published
2022-11-14
How to Cite
SADEEQ, M. I., OMAR, F. M., & PIRDAWOOD, M. A. (2022). NUMERICAL SOLUTION OF HIROTA-SATSUMA COUPLED KDV SYSTEM BY RBF-PS METHOD. Journal of Duhok University, 25(2), 164-175. https://doi.org/10.26682/sjuod.2022.25.2.15
Section
Pure and Engineering Sciences
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