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

Asifa Tassaddiq, Aasma Khalid, Muhammad Nawaz Naeem, Abdul Ghaffar, Faheem Khan, Samsul Ariffin Abdul Karim and Kottakkaran Sooppy Nisar
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Asifa Tassaddiq: College of Computer and Information Sciences, Majmaah University, Al-Majmaah 11952, Saudi Arabia
Aasma Khalid: Department of Mathematics, Government College Women University Faisalabad, Faisalabad 38023, Pakistan
Muhammad Nawaz Naeem: Department of Mathematics, Government College University Faisalabad, Faisalabad 38023, Pakistan
Abdul Ghaffar: Department of Mathematical Sciences, BUITEMS, Quetta 87300, Pakistan
Faheem Khan: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
Samsul Ariffin Abdul Karim: 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
Kottakkaran Sooppy Nisar: Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia

Mathematics, 2019, vol. 7, issue 11, 1-17

Abstract: 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 10 th order BVPs but also estimate from 1st derivative to 10 th 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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