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

Filomat ◽  
2012 ◽  
Vol 26 (6) ◽  
pp. 1233-1245 ◽  
Author(s):  
Arshad Khan ◽  
Talat Sultana
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Sixth Order ◽  
Point Boundary ◽  
Spline Method ◽  
Quintic Spline ◽  
Practical Usefulness ◽  
Special Case ◽  
Boundary Equations

In this paper, parametric quintic spline method is presented to solve a linear special case sixth order two point boundary value problems with two different cases of boundary conditions. The method presented in this paper has been shown to be second and fourth order accurate. Boundary equations are derived for both the cases of boundary conditions. Convergence analysis of these methods are discussed. The presented method is tested on four numerical examples of linear sixth order boundary value problems. Comparison is made to show the practical usefulness of the presented method.

scholarly journals Solving nonlinear third-order three-point boundary value problems by boundary shape functions methods

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ji Lin ◽  
Yuhui Zhang ◽  
Chein-Shan Liu
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Initial Conditions ◽  
Boundary Value ◽  
Accurate Solution ◽  
Point Boundary ◽  
Third Order ◽  
Boundary Shape ◽  
Free Function ◽  
New Algorithms

AbstractFor nonlinear third-order three-point boundary value problems (BVPs), we develop two algorithms to find solutions, which automatically satisfy the specified three-point boundary conditions. We construct a boundary shape function (BSF), which is designed to automatically satisfy the boundary conditions and can be employed to develop new algorithms by assigning two different roles of free function in the BSF. In the first algorithm, we let the free functions be complete functions and the BSFs be the new bases of the solution, which not only satisfy the boundary conditions automatically, but also can be used to find solution by a collocation technique. In the second algorithm, we let the BSF be the solution of the BVP and the free function be another new variable, such that we can transform the BVP to a corresponding initial value problem for the new variable, whose initial conditions are given arbitrarily and terminal values are determined by iterations; hence, we can quickly find very accurate solution of nonlinear third-order three-point BVP through a few iterations. Numerical examples confirm the performance of the new algorithms.

scholarly journals QSSOR and cubic non-polynomial spline method for the solution of two-point boundary value problems

2021 ◽  
Vol 2000 (1) ◽  
pp. 012007
Author(s):  
A Sunarto ◽  
P Agarwal ◽  
J V L Chew ◽  
H Justine ◽  
J Sulaiman
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Polynomial Spline ◽  
Point Boundary ◽  
Spline Method

Quintic spline solution of linear sixth-order boundary value problems

2007 ◽  
Vol 189 (1) ◽  
pp. 887-892 ◽  
Author(s):  
Shahid S. Siddiqi ◽  
Ghazala Akram ◽  
Saima Nazeer
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Sixth Order ◽  
Quintic Spline

Perturbation of two-point boundary value problems with eigenvalue parameter in the boundary conditions

1983 ◽  
Vol 94 (3-4) ◽  
pp. 213-219 ◽  
Author(s):  
Lawrence Turyn
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Boundary Value ◽  
Simple Eigenvalue ◽  
Point Boundary ◽  
Eigenvalue Parameter

SynopsisWe discuss smooth changes of eigenvalues under perturbation of the boundary value problems given in the title. The simple eigenvalue criterion is developed in the setting of Banach spaces, so very general perturbations of both the differential equation and the boundary conditions are allowed. Further, we need no assumptions about self-adjointness of the original or perturbed problems. The discussion is concluded with the application of the simple eigenvalue criterion to two examples.

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