Indian Journal of Science and Technology
Year: 2019, Volume: 12, Issue: 6, Pages: 1-9
Muhammad Abbas1*, Muhammad Kashif Iqbal2 , Bushra Zafar3 and Shazalina Binti Mat Zin4
1Department of Mathematics, University of Sargodha, Sargodha, Pakistan;
2Department of Mathematics, Government College University, Faisalabad, Pakistan;
3Department of Computer Science, Government College University, Faisalabad, Pakistan;
4Institute of Engineering Mathematics, Universiti Malaysia Perlis, Arau, Perlis;
*Author for correspondence
Department of Mathematics, University of Sargodha, Sargodha, Pakistan;
Email: [email protected]
Objectives: In this work, the approximate solution of non-linear third order Korteweg-de Vries equation has been studied. Methods: The proposed numerical technique engages finite difference formulation for temporal discretization, whereas, the discretization in space direction is achieved by means of a new cubic B-spline approximation. Findings: In order to corroborate this effort, three test problems have been considered and the computational outcomes are compared with the current methods. It is found that the proposed scheme involves straight forward computations and operates superior to the existing methods. Novelty/Improvements: The proposed numerical scheme is novel for Korteweg-de Vries equation and has never been employed for this purpose before.
Keywords: Cubic B-spline Collocation Method, Cubic B-spline Functions, Finite Difference Formulation, Korteweg-de Vries Equation
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