Linear Dependence Relations Connecting Equal Interval Nth Degree Splines and Their Derivatives

Successive polynomial spline function approximation

“…The quantities defined in equation (2.2), c~PN ) , have been studied by several authors ( [2], [3], [5]) and some of their properties are summarized in the following lemma. …”

Numerical Solution of Fifth Order Boundary Value Problems by Galerkin Method with Quartic B-splines

“…Davies A.R et al [1,2] were developed two numerical techniques namely, Spectral Galerkin and Spectral Collocation methods to solve fifth order boundary value problems, Fyfe [4] used spline functions to solve fifth order boundary value problems, who used quintic polynomial spline functions to develop consistency relation connecting the values of solution with fifth order derivative at the respective nodal points, Siddiqi et al [5] presented the solution of special case of fifth order boundary value problems by using quartic spline functions, Siddiqi and Gazala [6,7] presented the solution of special case of fifth order boundary value problems by using sextic polynomial and non-polynomial spline functions respectively, Rashidinia et al [8,9] developed the solution of fifth order boundary value problems with mixed boundary conditions and boundary conditions of the type (2) by using sextic B-spline Collocation method and non-polynomial sextic spline off step method respectively, Caglar et al [10] developed the solution of special type of fifth order boundary value problems by Collocation method with sixth degree B-splines, Siraj ul-Islam and Muhammad Azam Khan [11] presented the solution of special case of fifth order boundary value problems by using sextic spline functions, Feng-Gong Lang and Xiao-Ping Xu [12,13] developed the solution of special case of fifth order boundary value problems by using cubic and quartic B-spline Collocation methods respectively, Lamnii et al [14] applied sextic B-spline Collocation method to solve special case of fifth order boundary value problems, Kasi Viswanadham and Murali krishna [15] developed the quintic B-spline Galerkin method to solve special case of fifth order boundary value problems, Kasi Viswanadham and Showri raju [16,17] developed the cubic and quartic B-spline Collocation methods to solve fifth order boundary value problems, Kasi Viswanadham et al [18] developed the sextic B-spline Collocation method to solve special case of fifth order boundary value problems. So far, fifth order boundary value problems have not been solved by using Galerkin method with quartic B-splines.…”

Application of homotopy perturbation method to the fifth-order boundary value problems

“…The fifth-order boundary value problems which arise in the mathematical modeling of viscoelastic flows and other branches of mathematical, physical and engineering sciences, have been widely studied by many authors [5,6,8].…”