scholarly journals HYBRID CUBIC B-SPLINE METHOD FOR SOLVING NON-LINEAR TWO-POINT BOUNDARY VALUE PROBLEMS

2016 ◽  
Vol 110 (2) ◽  
Author(s):  
A.S. Heilat ◽  
A.I.Md. Ismail
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Point Boundary ◽  
Spline Method ◽  
B Spline ◽  
Non Linear

B-spline Method for Solving General Singularly Perturbed Boundary Value Problems Using Fitted Mesh

2006 ◽  
Vol 2 (4) ◽  
pp. 193-203
Author(s):  
M.K. Kadalbajoo ◽  
Vivek K. Aggarwal
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Uniform Mesh ◽  
Point Boundary ◽  
Spline Method ◽  
B Spline ◽  
Linear Problems ◽  
Mesh Technique ◽  
Quasilinearization Technique

In this paper we develop B-spline method for solving a class of Singularly Perturbed two point boundary value problems given as We use the Fitted mesh technique to generate piecewise uniform mesh, and use B-spline method which leads to a tridiagonal linear system. In case of non-linear problems we first linearize the equation using Quasilinearization technique and the resulting problem is solved by B-spline. The convergence analysis is given and the method is shown to have uniform convergence. Numerical illustrations are given in the end to demonstrate the efficiency of our method.

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 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
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