Numerical solution of sixth order boundary value problems with sixth degree B-spline functions

Parametric quintic spline solution for sixth order two point boundary value problems

“…Ritz's method based on variational theory [10] and variational iteration methods [16] have been applied for the solution of sixth order boundary value problems. M. El-Gamel et al [8] used Sinc-Galerkin method, Loghmani and Ahmadinia [13] used sixth degree B-spline functions, Ramadan et al [17] used septic nonpolynomial spline functions and Siddiqi and Akram [21] solved linear problem using polynomial septic spline solution for sixth order boundary value problems. Twizell and Boutayeb [25] developed a family of numerical methods for the solutions of special and general sixth order boundary value problems with application to Benard layer eigenvalue problems.…”

An effective method for numerical solution and numerical derivatives for sixth order two-point boundary value problems

“…Currently, there have been some numerical methods for (1.1). For example, the modified decomposition method [7], the homotopy perturbation method [8], the variational iteration method [9], the spline methods [10][11][12][13] and the fourth order finite difference method [14] have been pre sented by some scholars respectively. However, the error orders of some of these methods are not higher.…”

NTH-Degree Spline Method for Solving Dirichlet Condition (Dc) of Linear Ordinary Differential Equations (Odes)

“…Splines tend to be stapler than fitting a polynomial through the (N+1) points, with less possibility of wild oscillations between the tabulated points. [1], [4] In the present paper, a cubic b-spline is used to solve two point dirichlet conditions as following linear systems which are assumed to have a unique solution in the interval [0,1] (1) With dirichlet conditions y (0) =0 y (1) =0 Where m(x), n(x), and f(x) are continuous function, we suppose that n(x)=m(x)=1 In part (2), we have given the definition of Nth-degree spline, this method presents to approximate the solution of two point dirichlet conditions. In part (3) ,(4) and (5) we have solved problem using the method with two conditions In the last part, report the major conclusion and further developments.…”