scholarly journals Solution of a class of fourth order singular singularly perturbed boundary value problems by quintic B-spline method

2016 ◽  
Vol 35 (1) ◽  
pp. 257-265 ◽  
Author(s):  
Ram Kishun Lodhi ◽  
Hradyesh Kumar Mishra
Keyword(s):  
Boundary Value Problems ◽  
Fourth Order ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Spline Method ◽  
B Spline

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.

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