Abstract
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.
Highlights
It is frequently significant in practice to find estimated illustrations of physical data by comparatively simple mathematical functions
To validate the appropriateness of the proposed technique for solving the 8th order BVP’s, we considered six examples which are linear and non-linear BVP’s
Numerical outcomes for each problem are obtainable in tabular forms and matched with the exact solutions and absolute errors are calculated
Summary
It is frequently significant in practice to find estimated illustrations of physical data by comparatively simple mathematical functions. Polynomials have regularly been used for such mission, but it had been accepted that there were numerous kinds of data set for which polynomial approximations were unacceptable in that a very high degree may be mandatory to attain the essential accurateness. To overcome such complications attention has turned to the use of piece-wise polynomials or spline functions. Spline only means a piece-wise polynomial of degree k that is continuously differentiable k − 1 times. Spline interpolation is a formula of interpolation wherever the interpolate is a different kind of piece-wise polynomial called spline.
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