Numerical Solution of the Boundary Value Problems Arising in Magnetic Fields and Cylindrical Shells

Mathematics

Abdul Ghaffar¹  Dumitru Baleanu²  KottakkaranSooppy Nisar³  MuhammadNawaz Naeem⁴  Aasma Khalid⁴  MaysaaM. Al-Qurashi⁵  Zafar Ullah⁶ 

[1] Department of Mathematics, Balochistan University of Information Technology, Engineering and Management Sciences (BUITEMS), Quetta 87300, Pakistan;Department of Mathematics, Cankaya University, Ankara 06530, Turkey;Department of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia;Department of Mathematics, Government College University Faisalabad, Faisalabad 38023, Pakistan;Department of Mathematics, King Saud University, Riyadh 11495, Saudi Arabia;Department of Mathematics, University of Education, Campus DG Khan, Lahore 54770, Pakistan;

关键词: 8th order;    cubic B-spline;    numerical solution;    boundary value problems;    central finite difference approximations;    absolute error;    system of linear algebraic equations;   

DOI  :  10.3390/math7060508

来源: DOAJ

【 摘 要 】

This paper is devoted to the study of the Cubic B-splines to find the numerical solution of linear and non-linear 8th order BVPs that arises in the study of astrophysics, magnetic fields, astronomy, beam theory, cylindrical shells, hydrodynamics and hydro-magnetic stability, engineering, applied physics, fluid dynamics, and applied mathematics. The recommended method transforms the boundary problem to a system of linear equations. The algorithm we are going to develop in this paper is not only simply the approximation solution of the 8th order BVPs using Cubic-B spline but it also describes the estimated derivatives of 1st order to 8th order of the analytic solution. The strategy is effectively applied to numerical examples and the outcomes are compared with the existing results. The method proposed in this paper provides better approximations to the exact solution.

【 授权许可】

Unknown