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

被引：15

作者：

Tassaddiq, Asifa ^{[1
]}

Khalid, Aasma ^{[2
,3
]}

Naeem, Muhammad Nawaz ^{[3
]}

Ghaffar, Abdul ^{[4
]}

Khan, Faheem ^{[5
]}

Karim, Samsul Ariffin Abdul ^{[6
,7
]}

Nisar, Kottakkaran Sooppy ^{[8
]}

机构：

[1] Majmaah Univ, Coll Comp & Informat Sci, Al Majmaah 11952, Saudi Arabia

[2] Govt Coll Women Univ Faisalabad, Dept Math, Faisalabad 38023, Pakistan

[3] Govt Coll Univ Faisalabad, Dept Math, Faisalabad 38023, Pakistan

[4] BUITEMS, Dept Math Sci, Quetta 87300, Pakistan

[5] Univ Sargodha, Dept Math, Sargodha 40100, Pakistan

[6] Univ Teknol Petronas, Inst Autonomous Syst, Fundamental & Appl Sci Dept, Seri Iskandar 32610, Perak Darul Rid, Malaysia

[7] Univ Teknol Petronas, Inst Autonomous Syst, Ctr Smart Grid Energy Res CSMER, Seri Iskandar 32610, Perak Darul Rid, Malaysia

[8] Prince Sattam bin Abdulaziz Univ, Coll Arts & Sci, Dept Math, Wadi Aldawaser 11991, Saudi Arabia

来源：

MATHEMATICS | 2019年 / 7卷 / 11期

关键词：

non-linear differential equation; cubic B-spline; central finite difference approximations; absolute errors; BOUNDARY-VALUE-PROBLEMS; RELIABLE ALGORITHM; NUMERICAL-SOLUTION; ORDER;

D O I：

10.3390/math7111078

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：17

共 8 条

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