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Numerical Solution of Fifth Order Boundary Value Problems by Galerkin Method with Quartic B-splines

by K. N. S. Kasi Viswanadham, Sreenivasulu Ballem
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 77 - Number 17
Year of Publication: 2013
Authors: K. N. S. Kasi Viswanadham, Sreenivasulu Ballem
10.5120/13613-1382

K. N. S. Kasi Viswanadham, Sreenivasulu Ballem . Numerical Solution of Fifth Order Boundary Value Problems by Galerkin Method with Quartic B-splines. International Journal of Computer Applications. 77, 17 ( September 2013), 7-12. DOI=10.5120/13613-1382

@article{ 10.5120/13613-1382,
author = { K. N. S. Kasi Viswanadham, Sreenivasulu Ballem },
title = { Numerical Solution of Fifth Order Boundary Value Problems by Galerkin Method with Quartic B-splines },
journal = { International Journal of Computer Applications },
issue_date = { September 2013 },
volume = { 77 },
number = { 17 },
month = { September },
year = { 2013 },
issn = { 0975-8887 },
pages = { 7-12 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume77/number17/13613-1382/ },
doi = { 10.5120/13613-1382 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:50:16.663893+05:30
%A K. N. S. Kasi Viswanadham
%A Sreenivasulu Ballem
%T Numerical Solution of Fifth Order Boundary Value Problems by Galerkin Method with Quartic B-splines
%J International Journal of Computer Applications
%@ 0975-8887
%V 77
%N 17
%P 7-12
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

A finite element method involving Galerkin method with quartic B-splines as basis functions has been developed to solve a general fifth order boundary value problem. The basis functions are redefined into a new set of basis functions which vanish on the boundary where Dirichlet type of boundary conditions and Neumann boundary conditions are prescribed. The proposed method was applied to solve several examples of fifth order linear and nonlinear boundary value problems. The solution of a non-linear boundary value problem has been obtained as the limit of a sequence of solution of linear boundary value problems generated by quasilinearization technique. The obtained numerical results are compared with the exact solutions available in the literature.

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Index Terms

Computer Science
Information Sciences

Keywords

Galerkin method Quartic B-spline Basis function Fifth order boundary value problem Absolute error.

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