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Numerical Solution of Eighth Order Boundary Value Problems by Galerkin Method with Quintic B-splines

by K.n.s. Kasi Viswanadham, Sreenivasulu Ballem
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 89 - Number 15
Year of Publication: 2014
Authors: K.n.s. Kasi Viswanadham, Sreenivasulu Ballem
10.5120/15705-4562

K.n.s. Kasi Viswanadham, Sreenivasulu Ballem . Numerical Solution of Eighth Order Boundary Value Problems by Galerkin Method with Quintic B-splines. International Journal of Computer Applications. 89, 15 ( March 2014), 7-13. DOI=10.5120/15705-4562

@article{ 10.5120/15705-4562,
author = { K.n.s. Kasi Viswanadham, Sreenivasulu Ballem },
title = { Numerical Solution of Eighth Order Boundary Value Problems by Galerkin Method with Quintic B-splines },
journal = { International Journal of Computer Applications },
issue_date = { March 2014 },
volume = { 89 },
number = { 15 },
month = { March },
year = { 2014 },
issn = { 0975-8887 },
pages = { 7-13 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume89/number15/15705-4562/ },
doi = { 10.5120/15705-4562 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:09:18.436402+05:30
%A K.n.s. Kasi Viswanadham
%A Sreenivasulu Ballem
%T Numerical Solution of Eighth Order Boundary Value Problems by Galerkin Method with Quintic B-splines
%J International Journal of Computer Applications
%@ 0975-8887
%V 89
%N 15
%P 7-13
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, we present a finite element method involving Galerkin method with quintic B-splines as basis functions to solve a general eighth order two point 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, Neumann boundary conditions, second order derivative boundary conditions and third order derivative type of boundary conditions are prescribed. The proposed method was applied to solve several examples of the eighth order linear and nonlinear boundary value problems. The solution of a nonlinear 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 exact solutions available in the literature.

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Index Terms

Computer Science
Information Sciences

Keywords

Galerkin method Quintic B-spline Basis function Eighth order boundary value problem Absolute error.