Numerical Solution of Modified Forms of Camassa-Holm and Degasperis-Procesi Equations via Quartic B-Spline Collocation Method

Authors

  • Imtiaz Wasim Department of Mathematics, University of Sargodha, Sargodha
  • Muhammad Abbas Department of Mathematics, University of Sargodha, Sargodha
  • Muhammad Kashif Iqbal Department of Mathematics, GC University, Faisalabad

DOI:

https://doi.org/10.26713/cma.v9i3.803

Keywords:

Non-linear modified Camassa-Holm and Degasperis-Procesi equations, Quartic B-spline collocation method, Convergence

Abstract

In this paper, a collocation finite difference scheme based on Quartic B-spline function is developed for solving non-linear modified Camassa-Holm and Degasperis-Procesi equations. A finite difference scheme and Quartic B-spline function are used to discretize the time and spatial derivatives, respectively. The obtained numerical results are compared with the exact analytical solutions and some methods existing in literature. The numerical solutions of proposed non-linear equations are acquired without any linearization technique. The convergence of the method is proved of order \((\Delta t + h^2)\). The efficiency of the proposed scheme is demonstrated through illustrative examples. The presented scheme is realized to be a very reliable alternate method to some existing schemes for such physical problems.

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Published

25-09-2018
CITATION

How to Cite

Wasim, I., Abbas, M., & Iqbal, M. K. (2018). Numerical Solution of Modified Forms of Camassa-Holm and Degasperis-Procesi Equations via Quartic B-Spline Collocation Method. Communications in Mathematics and Applications, 9(3), 393–409. https://doi.org/10.26713/cma.v9i3.803

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Research Article