Cubic Spline Solution of linear fourteenth order boundary value problems

Aasma Khalid A,M Nawaz Naeem

doi:10.4038/cjs.v47i3.7541

Abstract

As higher order differential equations have constantly been tiresome and problematic to resolve for the mathematicians and engineers so diverse numerical procedures were conceded out to acquire numerical estimates to such problems. In this paper an innovative numerical procedure is developed to estimate the fourteenth-order boundary value problems (BVPs) using Polynomial and Non-Polynomial Cubic spline. The procedures adopted in our work are based on cubic polynomial and non-polynomial spline method together with the decomposition procedure. In this paper polynomial and non-polynomial cubic splines along with the finite difference approximations will be used to squeeze the system of second order Boundary Value Problems in such a way that it will be converted into to a system consists of linear algebraic equations along with boundary conditions. These strategies will be operated on two problems to evidence the handiness of the technique by means of step size h = 1/5. The exactness of this method for detailed investigation is equated with the precise solution and conveyed through tables.

Highlights

Been tiresome and problematic to resolve for the mathematicians and engineers so diverse numerical procedures were conceded = out u(2i) (a) j= i =, u(2ui)(2i()b)(a) ki j= i,(2) u(2i) (b) ki (2) to acquire numerical estimates to such problems
Up-to-date studies in hydrodynamic and hydro magnetic stability have exposed the presence of a class of characteristic-value problems in differential equations of high order which have genuine mathematical concern
A numerical procedure with polynomial and non- gordon” equation was solved by non-polynomial cubic polynomial cubic splines have been established for spline

Summary

Where α

In order to originate non-polynomial spline estimate S to (4) beside with the boundary conditions given in (j5j), we distribute the interval[a, b]into n identical subintervals by means of grid points:.

To demonstrate how the method is applied as urbanized in

Numerical applications

Cubic Polynomial absolute error

Solution absolute absolute error reletive error reletive error error

Spline Method for One Dimensional Nonlinear