CFP last date
20 December 2024
Call for Paper
January Edition
IJCA solicits high quality original research papers for the upcoming January edition of the journal. The last date of research paper submission is 20 December 2024

Submit your paper
Know more
The week's pick
Responsive image
Improved Shuffled Frog Leaping Algorithm with Self-Adaptive Shuffling for Fuzzy Logic PD+G Controller Optimization in Robotic Manipulators

Duc Hoang Nguyen
Random Articles
Reseach Article

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

by K. N. S. Kasi Viswanadham, Sreenivasulu Ballem
journal cover thumbnail

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.

References
  1. Davies, A. R. , Karageorghis. , and Phillips. Spectral Galerkin Methods for the primary two point boundary value problem in modeling viscoealastics flows. International Journal of Numerical Methods in Engineering. 26 (1988), 647-662.
  2. Davies, A. R. , Karageorghis. , and Phillips. Spectral Collocation Methods for the primary two point boundary value problem in modeling viscoealastics flows. International Journal of Numerical Methods in Engineering. 26 (1988), 805-813.
  3. Agarwal, R. P. 1986 Boundary value problems for higher order differential equations. World Scientific, Singapore.
  4. Fyfe, D. J. Linear dependence relations connecting equal interval Nth degree splines and their derivatives. Journal of the Institute of Mathematics and its Applications. 7 (1971), 398-406.
  5. Shahid, S. Siddiqi. , Ghazala, Akram. , and Arfa, Elahi. 2008. Quartic spline solutions of linear fifth order boundary value problems. Applied Mathematics and Computation. 196 (2008), 214-220.
  6. Shahid, S. Siddiqi. , and Ghazala, Akram. Sextic spline solutions of fifth order boundary value problems. Applied Mathematics Letters. 20 (2007), 591-597.
  7. Shahid, S. Siddiqi. , and Ghazala, Akram. Solution of fifth order boundary value problems using non-polynomial spline technique. Applied Mathematics and Computation. 175 (2006), 1574-1581.
  8. Rashidinia, J. , Jalilian, R. , and Ghasemi, M. An O(h6) numerical solution of general nonlinear fifth order two point boundary value problems. Numerical Algorithms. 55 (2010), 403-428.
  9. Rashidinia, J. , Jalilian, R. , and Farajeyan, K. Non-polynomial spline approach to the solution of fifth-order boundary value problems. Journal of Information and Computing Science. 4 (2009), 265-274.
  10. Hikmet, Caglar. , Nazan, Caglar. , and Twizell. The numerical solution of fifth order boundary value problems with sixth degree B-spline functions. Applied Mathematics Letter. 12 (1999), 25-30.
  11. Siraj-ul-Islam. , and Muhammad, Azam, Khan. A numerical method based on polynomial sextic spline functions for the solution of special fifth order boundary value problems. Applied Mathematics and Computation. 181 (2006), 356-361.
  12. Feng-Gong, Lang. , and Xiao-Ping, Xu. A new cubic B-Spline method for linear fifth order boundary value problems. Journal of Computational and Applied Mathematics. 36 (2011), 101-116.
  13. Feng-Gong, Lang. , and Xiao-Ping ,Xu. Quartic B-Spline Collocation method for fifth order boundary value problems. Computing. 92 (2011), 365-378.
  14. Lamnii, A. , Mraoui. , and Tijini, A. Sextic spline solution of fifth-order boundary value problems. Mathematics and Computers in Simulation. 77(2008), 237-246.
  15. Kasi, Viswanadham, K. N. S. , and Murali, Krishna, P. Quintic B-splines Galerkin for fifth order boundary value problems. ARPN Journal of Engineering and Applied Sciences. 5(2010), 74-77.
  16. Kasi, Viswanadham, K. N. S. , and Showri, Raju, Y. Cubic B-spline Collocation method for fifth boundary value problems. International Journal for Mathematical Sciences and Engineering Applications. 6(2012), 431-447.
  17. Kasi, Viswanadham, K. N. S. , and Showri, Raju, Y. Quartic B-spline Collocation method for fifth boundary value problems. International Journal of Computer Applications. 3 (2012), 1-6.
  18. Kasi, Viswanadham, K. N. S. , Murali, Krishna, P. , and Prabhakara, Rao, C. Numerical solution of fifth order boundary value problems by Collocation method with sixth order B-splines. International Journal of Applied Science and Engineering. 8 (2010), 119-125.
  19. Bellman, R. E. , and Kalabaa, R. E. , 1965 Quasilinearzation and Nonlinear boundary value problems. American Elsevier, New York.
  20. Bers, L. , John, F. , and Schecheter, M. 1964 Partial differential equations. John Wiley Inter Science, New York.
  21. Lions, J. L. , and Magenes, E. 1972 Non-Homogeneous boundary value problem and applications. Springer-Verlag, Berlin.
  22. Mitchel, A. R. , and Wait, R. 1977 The finite flement method in partial differential equations. John Wiley and Sons, London.
  23. Prenter, P. M. 1989 Splines and variational methods. John Wiley and Sons, New York.
  24. Carl, de-Boor, 2001 A pratical guide to splines. Springer-Verlag.
  25. Schoenberg, I. J. 1966 On Spline Functions, MRC Report 625. University of Wisconsin.
Index Terms

Computer Science
Information Sciences

Keywords

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

Powered by PhDFocusTM