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Numerical Solution of Fourth Order Boundary Value Problems by Petrov-Galerkin Method with Cubic B-splines as basis Functions and Quintic B-Splines as Weight Functions

by K.n.s.kasi Viswanadham, S.m.reddy
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 104 - Number 6
Year of Publication: 2014
Authors: K.n.s.kasi Viswanadham, S.m.reddy
10.5120/18208-9348

K.n.s.kasi Viswanadham, S.m.reddy . Numerical Solution of Fourth Order Boundary Value Problems by Petrov-Galerkin Method with Cubic B-splines as basis Functions and Quintic B-Splines as Weight Functions. International Journal of Computer Applications. 104, 6 ( October 2014), 37-43. DOI=10.5120/18208-9348

@article{ 10.5120/18208-9348,
author = { K.n.s.kasi Viswanadham, S.m.reddy },
title = { Numerical Solution of Fourth Order Boundary Value Problems by Petrov-Galerkin Method with Cubic B-splines as basis Functions and Quintic B-Splines as Weight Functions },
journal = { International Journal of Computer Applications },
issue_date = { October 2014 },
volume = { 104 },
number = { 6 },
month = { October },
year = { 2014 },
issn = { 0975-8887 },
pages = { 37-43 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume104/number6/18208-9348/ },
doi = { 10.5120/18208-9348 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:35:27.893156+05:30
%A K.n.s.kasi Viswanadham
%A S.m.reddy
%T Numerical Solution of Fourth Order Boundary Value Problems by Petrov-Galerkin Method with Cubic B-splines as basis Functions and Quintic B-Splines as Weight Functions
%J International Journal of Computer Applications
%@ 0975-8887
%V 104
%N 6
%P 37-43
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This paper deals with a finite element method involving Petrov-Galerkin method with cubic B-splines as basis functions and quintic B-splines as weight functions to solve a general fourth 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 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 fourth 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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Index Terms

Computer Science
Information Sciences

Keywords

Petrov-Galerkin method Cubic B-spline Quintic B-spline Fourth order boundary value problem Absolute error.

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