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Open AccessArticle

A New Scheme Using Cubic B-Spline to Solve Non-Linear Differential Equations Arising in Visco-Elastic Flows and Hydrodynamic Stability Problems

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College of Computer and Information Sciences, Majmaah University, Al-Majmaah 11952, Saudi Arabia
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Department of Mathematics, Government College Women University Faisalabad, Faisalabad 38023, Pakistan
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Department of Mathematics, Government College University Faisalabad, Faisalabad 38023, Pakistan
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Department of Mathematical Sciences, BUITEMS, Quetta 87300, Pakistan
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Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
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Fundamental and Applied Sciences Department and Centre for Smart Grid Energy Research (CSMER), Institute of Autonomous System, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, Seri Iskandar 32610, Perak Darul Ridzuan, Malaysia
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Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1078; https://doi.org/10.3390/math7111078
Received: 4 August 2019 / Revised: 27 October 2019 / Accepted: 28 October 2019 / Published: 8 November 2019
This study deals with the numerical solution of the non-linear differential equations (DEs) arising in the study of hydrodynamics and hydro-magnetic stability problems using a new cubic B-spline scheme (CBS). The main idea is that we have modified the boundary value problems (BVPs) to produce a new system of linear equations. The algorithm developed here is not only for the approximation solutions of the 10th order BVPs but also estimate from 1st derivative to 10th derivative of the exact solution as well. Some examples are illustrated to show the feasibility and competence of the proposed scheme.
Keywords: non-linear differential equation; cubic B-spline; central finite difference approximations; absolute errors non-linear differential equation; cubic B-spline; central finite difference approximations; absolute errors
MDPI and ACS Style

Tassaddiq, A.; Khalid, A.; Naeem, M.N.; Ghaffar, A.; Khan, F.; Karim, S.A.A.; Nisar, K.S. A New Scheme Using Cubic B-Spline to Solve Non-Linear Differential Equations Arising in Visco-Elastic Flows and Hydrodynamic Stability Problems. Mathematics 2019, 7, 1078.

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