Numerical Solution of Seventh Order Boundary Value Problems by Petrov-Galerkin Method with Quintic B-splines as Basis Functions and Septic B-splines as Weight Functions

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International Journal of Computer Applications
© 2015 by IJCA Journal
Volume 122 - Number 5
Year of Publication: 2015
Authors:
K. N. S. Kasi Viswanadham
S. M. Reddy
10.5120/21700-4811

K.n.s.kasi Viswanadham and S.m.reddy. Article: Numerical Solution of Seventh Order Boundary Value Problems by Petrov-Galerkin Method with Quintic B-splines as Basis Functions and Septic B-splines as Weight Functions. International Journal of Computer Applications 122(5):41-47, July 2015. Full text available. BibTeX

@article{key:article,
	author = {K.n.s.kasi Viswanadham and S.m.reddy},
	title = {Article: Numerical Solution of Seventh Order Boundary Value Problems by Petrov-Galerkin Method with Quintic B-splines as Basis Functions and Septic B-splines as Weight Functions},
	journal = {International Journal of Computer Applications},
	year = {2015},
	volume = {122},
	number = {5},
	pages = {41-47},
	month = {July},
	note = {Full text available}
}

Abstract

In this paper a finite element method involving Petrov-Galerkin method with quintic B-splines as basis functions and septic B-splines as weight functions has been developed to solve a general seventh order boundary value problem with a particular case of boundary conditions. The basis functions are redefined into a new set of basis functions which vanish on the boundary where the Dirichlet and the Neumann type of boundary conditions are prescribed. The weight functions are also redefined into a new set of weight functions which in number match with the number of redefined basis functions. The proposed method was applied to solve several examples of seventh order linear and nonlinear boundary value problems. The obtained numerical results were found to be in good agreement with the exact solutions available in the literature.

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