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Quartic B-Spline Collocation Method for Fifth Order Boundary Value Problems

by K. N. S. Kasi Viswanadham, Y. Showri Raju
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 43 - Number 13
Year of Publication: 2012
Authors: K. N. S. Kasi Viswanadham, Y. Showri Raju
10.5120/6160-8566

K. N. S. Kasi Viswanadham, Y. Showri Raju . Quartic B-Spline Collocation Method for Fifth Order Boundary Value Problems. International Journal of Computer Applications. 43, 13 ( April 2012), 1-6. DOI=10.5120/6160-8566

@article{ 10.5120/6160-8566,
author = { K. N. S. Kasi Viswanadham, Y. Showri Raju },
title = { Quartic B-Spline Collocation Method for Fifth Order Boundary Value Problems },
journal = { International Journal of Computer Applications },
issue_date = { April 2012 },
volume = { 43 },
number = { 13 },
month = { April },
year = { 2012 },
issn = { 0975-8887 },
pages = { 1-6 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume43/number13/6160-8566/ },
doi = { 10.5120/6160-8566 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:33:16.221678+05:30
%A K. N. S. Kasi Viswanadham
%A Y. Showri Raju
%T Quartic B-Spline Collocation Method for Fifth Order Boundary Value Problems
%J International Journal of Computer Applications
%@ 0975-8887
%V 43
%N 13
%P 1-6
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

A finite element method involving collocation method with quartic B-splines as basis functions have been developed to solve fifth order boundary value problems. The fifth order and fourth order derivatives for the dependent variable are approximated by the central differences of third order derivatives. The basis functions are redefined into a new set of basis functions which in number match with the number of collocated points selected in the space variable domain. The proposed method is tested on four linear and two non-linear boundary value problems. The solution of a non-linear boundary value problem has been obtained as the limit of a sequence of solutions of linear boundary value problems generated by quasilinearization technique. Numerical results obtained by the present method are in good agreement with the exact solutions available in the literature.

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Index Terms

Computer Science
Information Sciences

Keywords

Collocation Method Quartic B-spline Basis Function Fifth Order Boundary Value Problem Absolute Error

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