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Numerical solution of the Rosenau-KdV-RLW equation by using RBFs collocation method

Author

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  • Bahar Korkmaz

    (Department of Mathematics, Anadolu University, Eskişehir 26470, Turkey)

  • Yilmaz Dereli

    (Department of Mathematics, Anadolu University, Eskişehir 26470, Turkey)

Abstract

In this study, a meshfree method based on the collocation with radial basis functions (RBFs) is proposed to solve numerically an initial-boundary value problem of Rosenau-KdV-regularized long-wave (RLW) equation. Numerical values of invariants of the motion are computed to examine the fundamental conservative properties of the equation. Computational experiments for the simulation of solitary waves examine the accuracy of the scheme in terms of error norms L2 and L∞. Linear stability analysis is investigated to determine whether the present method is stable or unstable. The scheme gives unconditionally stable, and second-order convergent. The obtained results are compared with analytical solution and some other earlier works in the literature. The presented results indicate the accuracy and efficiency of the method.

Suggested Citation

  • Bahar Korkmaz & Yilmaz Dereli, 2016. "Numerical solution of the Rosenau-KdV-RLW equation by using RBFs collocation method," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(10), pages 1-11, October.
    • Handle: RePEc:wsi:ijmpcx:v:27:y:2016:i:10:n:s0129183116501175
    DOI: 10.1142/S0129183116501175
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