Collocation method with quintic b-spline method for solving hirota-satsuma coupled KDV equation

Authors

  • K. R. Raslan

  • Talaat S. El-Danaf

  • Khalid K. Ali

    Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt.

Received date: April 18, 2016

Accepted date: May 10, 2016

Published date: May 17, 2016

DOI:

https://doi.org/10.14419/ijamr.v5i2.6138

Keywords:

Collocation Method, Quintic B-Splines Method, Coupled KDV Equation

Abstract

In the present paper, a numerical method is proposed for the numerical solution of a coupled system of KdV (CKdV) equation with appropriate initial and boundary conditions by using collocation method with quintic B-spline on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms, are computed. Three invariants of motion are predestined to determine the preservation properties of the problem, and the numerical scheme leads to careful and active results. Furthermore, interaction of two and three solitary waves is shown. These results show that the technique introduced here is easy to apply. We make linearization for the nonlinear term.

References

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How to Cite

Raslan, K. R., El-Danaf, T. S., & Ali, K. K. (2016). Collocation method with quintic b-spline method for solving hirota-satsuma coupled KDV equation. International Journal of Applied Mathematical Research, 5(2), 123-131. https://doi.org/10.14419/ijamr.v5i2.6138

Received date: April 18, 2016

Accepted date: May 10, 2016

Published date: May 17, 2016