scholarly journals Extended cubic B-spline method for solving a linear system of second-order boundary value problems

SpringerPlus ◽  
2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Ahmed Salem Heilat ◽  
Nur Nadiah Abd Hamid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Linear System ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Spline Method ◽  
B Spline

scholarly journals Solution of Boundary Value Problems by Approaching Spline Techniques

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
P. Kalyani ◽  
P. S. Rama Chandra Rao
Keyword(s):  
Boundary Value Problems ◽  
Spline Function ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
Spline Method ◽  
B Spline ◽  
Numerical Examples ◽  
Specific Choice ◽  
Nodal Points

In the present work a nonpolynomial spline function is used to approximate the solution of the second order two point boundary value problems. The classes of numerical methods of second order, for a specific choice of parameters involved in nonpolynomial spline, have been developed. Numerical examples are presented to illustrate the applications of this method. The solutions of these examples are found at the nodal points with various step sizes and with various parameters (α, β). The absolute errors in each example are estimated, and the comparison of approximate values, exact values, and absolute errors of at the nodal points are shown graphically. Further, shown that nonpolynomial spline produces accurate results in comparison with the results obtained by the B-spline method and finite difference method.

scholarly journals Cubic Hermite Collocation Method for Solving Boundary Value Problems with Dirichlet, Neumann, and Robin Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Ishfaq Ahmad Ganaie ◽  
Shelly Arora ◽  
V. K. Kukreja
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Spline Method ◽  
Orthogonal Collocation ◽  
Nonlinear Boundary Value Problems ◽  
B Spline ◽  
Linear And Nonlinear ◽  
Volume Method

Cubic Hermite collocation method is proposed to solve two point linear and nonlinear boundary value problems subject to Dirichlet, Neumann, and Robin conditions. Using several examples, it is shown that the scheme achieves the order of convergence as four, which is superior to various well known methods like finite difference method, finite volume method, orthogonal collocation method, and polynomial and nonpolynomial splines and B-spline method. Numerical results for both linear and nonlinear cases are presented to demonstrate the effectiveness of the scheme.

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