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Quintic B-Spline Collocation Method for Tenth 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 51 - Number 15
Year of Publication: 2012
Authors: K. N. S. Kasi Viswanadham, Y. Showri Raju
10.5120/8116-1735

K. N. S. Kasi Viswanadham, Y. Showri Raju . Quintic B-Spline Collocation Method for Tenth Order Boundary Value Problems. International Journal of Computer Applications. 51, 15 ( August 2012), 7-13. DOI=10.5120/8116-1735

@article{ 10.5120/8116-1735,
author = { K. N. S. Kasi Viswanadham, Y. Showri Raju },
title = { Quintic B-Spline Collocation Method for Tenth Order Boundary Value Problems },
journal = { International Journal of Computer Applications },
issue_date = { August 2012 },
volume = { 51 },
number = { 15 },
month = { August },
year = { 2012 },
issn = { 0975-8887 },
pages = { 7-13 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume51/number15/8116-1735/ },
doi = { 10.5120/8116-1735 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:50:27.439619+05:30
%A K. N. S. Kasi Viswanadham
%A Y. Showri Raju
%T Quintic B-Spline Collocation Method for Tenth Order Boundary Value Problems
%J International Journal of Computer Applications
%@ 0975-8887
%V 51
%N 15
%P 7-13
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

A finite element method involving collocation method with quintic B-splines as basis functions has been developed to solve tenth order boundary value problems. The fifth order, sixth order, seventh order, eighth order, ninth order and tenth order derivatives for the dependent variable are approximated by the central differences of fourth order derivatives. The basis functions are redefined into a new set of basis functions which in number match with the number of selected collocated points in the space variable domain. The proposed method is tested on several linear and 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 Quintic B-spline Basis Function Tenth Order Boundary Value Problem Absolute Error

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