Numerical approximation for the solution of linear sixth order boundary value problems by cubic B-spline

A Khalid,S Jain,A Ghaffar,M N Naeem,P Agarwal,Z Ullah

doi:10.1186/s13662-019-2385-9

Abstract

In the current paper, authors proposed a computational model based on the cubic B-spline method to solve linear 6th order BVPs arising in astrophysics. The prescribed 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 6th order BVPs using cubic B-spline, but it also describes the estimated derivatives of 1st order to 6th order of the analytic solution at the same time. This novel technique has lesser computational cost than numerous other techniques and is second order convergent. To show the efficiency of the proposed method, four numerical examples have been tested. The results are described using error tables and graphs and are compared with the results existing in the literature.

Highlights

The applications of boundary value problems (BVPs) are almost unlimited, and they play an important role in all the branches of science, engineering, and technology
We will study the algebraic results of the following linear 6th order BVP: w(6)(z) + a1(z)w(5)(z) + a2(z)w(4)(z) + a3(z)w(3)(z)
2 Materials and methods the fundamentals of cubic B-spline and its application on sixth order BVP are discussed in detail

Summary

Introduction

The applications of boundary value problems (BVPs) are almost unlimited, and they play an important role in all the branches of science, engineering, and technology. They are applied to model many systems in several fields of science and engineering. There has been significant advancement in solving problems related to a system of linear and nonlinear partial and ordinary differential equations concerning boundary conditions (BC). Two point nonlinear BVPs often cannot be solved by analytical techniques. With cumulative interest in finding solutions to linear/nonlinear BVPs has come an increasing requirement for solution techniques. We will study the algebraic results of the following linear 6th order BVP: w(6)(z) + a1(z)w(5)(z) + a2(z)w(4)(z) + a3(z)w(3)(z)

Methods

Results

Conclusion