We apologize for a recent technical issue with our email system, which temporarily affected account activations. Accounts have now been activated. Authors may proceed with paper submissions. PhDFocusTM
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

A Comparative Study of Galerkin Finite Element and B-Spline Methods for Two Point Boundary Value Problems

by Dinkar Sharma, Sangeeta Arora, Sheo Kumar
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 67 - Number 23
Year of Publication: 2013
Authors: Dinkar Sharma, Sangeeta Arora, Sheo Kumar
10.5120/11532-5386

Dinkar Sharma, Sangeeta Arora, Sheo Kumar . A Comparative Study of Galerkin Finite Element and B-Spline Methods for Two Point Boundary Value Problems. International Journal of Computer Applications. 67, 23 ( April 2013), 1-6. DOI=10.5120/11532-5386

@article{ 10.5120/11532-5386,
author = { Dinkar Sharma, Sangeeta Arora, Sheo Kumar },
title = { A Comparative Study of Galerkin Finite Element and B-Spline Methods for Two Point Boundary Value Problems },
journal = { International Journal of Computer Applications },
issue_date = { April 2013 },
volume = { 67 },
number = { 23 },
month = { April },
year = { 2013 },
issn = { 0975-8887 },
pages = { 1-6 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume67/number23/11532-5386/ },
doi = { 10.5120/11532-5386 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:26:12.133192+05:30
%A Dinkar Sharma
%A Sangeeta Arora
%A Sheo Kumar
%T A Comparative Study of Galerkin Finite Element and B-Spline Methods for Two Point Boundary Value Problems
%J International Journal of Computer Applications
%@ 0975-8887
%V 67
%N 23
%P 1-6
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In chemical engineering, deflection of beams and other area of engineering the two point boundary value problems with Neumann and mixed Robbin's boundary conditions have great importance. It is not easy task to solve numerically such type of problems. In this study a B-spline finite element has been introduced to get the solution of two point boundary value problem. Some test examples are considered for the applicability of the purposed scheme. Further the results are compared with simple Galerkin-finite element method and with the exact solution of the problems. Throughout the discussion, it is observed that the proposed technique is performing well.

References
  1. Jang B (2008). Two-point boundary value problems by the extended Adomian decomposition method. Journal of Computational and Applied Mathematics 219(1), pp. 253-262.
  2. Brenner H (1962). The diffusion model of longitudinal mixing in beds of finite length. Numerical values. Chemical Engineering Science 17(4), pp. 229-243.
  3. Sharma D, Jiwari R and Kumar S (2011). Galerkin-finite element methods for numerical solution of advection- diffusion equation. International Journal of Pure and Applied Mathematics 70(3), pp. 389-399.
  4. Noye BJ (1990). Numerical solution of partial differential equations, Lecture Notes.
  5. Dogan A (2004). A Galerkin finite element approach of Burgers' equation. Applied Mathematics and Computation 157(2), pp. 331-346.
  6. Sengupta TK, Talla SB and Pradhan SC (2005). Galerkin finite element methods for wave problems. Sadhana 30(5), pp. 611-623.
  7. Kaneko H, Bey KS and Hou GJW (2006). Discontinuous Galerkin finite element method for parabolic problems. Applied Mathematics and Computation 182(1), pp. 388-402.
  8. EI-Gebeily MA, Furati KM and O'Regan D (2009). The finite element-Galerkin method for singular self-adjoint differential equations. Journal of Computational and Applied Mathematics 223(2), pp. 735-752.
  9. Jangveladze T, Kiguradze Z and Neta B (2011). Galerkin finite element method for one nonlinear integro-differential model. Applied Mathematics and Computation 217(16), pp. 6883-6892.
  10. Padmaja P, Chakravarthy PP and Reddy YN (2012). A nonstandard explicit method for solving singularly perturbed two point boundary value problems via method of reduction of order. International Journal of Applied Mathematics and Mechanics 8(2), pp. 62-76.
  11. Kumar R, Kumar S and Miglani A (2010). Boundary value problem in fluid saturated incompressible porous medium due to inclined load. International Journal of Applied Mathematics and Mechanics 6(13), pp. 11-27.
  12. Shabani MO and Mazahery A (2011). Application of finite element method for simulation of mechanical properties in A356 alloy. International Journal of Applied Mathematics and Mechanics 7 (5), pp. 89-97.
  13. Pathak AK and Doctor HD (2011). Comparison of collocation method â€" spline, finite difference and finite element method for solving two dimensional parabolic partial differential equation. International Journal of Applied Mathematics and Mechanics 7(18), pp. 56-68.
  14. Mittal RC and Jiwari R (2009). Numerical study of burger-huxley equation by differential quadrature method. International Journal of Applied Mathematics and Mechanics 5(8), pp. 1-9.
  15. Chun C and Sakthivel R (2010). Homotopy perturbation technique for solving two-point boundary value problems- comparison with other methods. Computer Physics Communications. 181 (6), pp. 1021-1024.
  16. Keller H B (1968). Numerical methods for Two-point boundary value problems. Blaisdell Mass.
  17. Sharma D, Jiwari R and Kumar S (2012). Numerical solution of two-point boundary value problems using Galerkin-Finite element method. International Journal of Non-linear Science. 13(2), pp. 204-210.
  18. Fox L (1957). The numerical solution of Two-point boundary value problems in ordinary differential equations. Oxford University Press.
  19. Bellman R E and Kalaba R E (1965). Quasilinearization and nonlinear boundary value problems. Rand Corp.
  20. Sharma D, Jiwari R and Kumar S (2012). A comparative study of Model matrix and Finite element methods for two-point boundary value problems. International Journal of Applied Mathematics and Mechanics 8 (13), pp. 29-45.
  21. Lee E S (1968). Quasilinearization and invariant imbedding. Academic Press, New York.
Index Terms

Computer Science
Information Sciences

Keywords

Finite Element Method B-Spline Dirichlet's boundary conditions Mixed Robbin's Boundary Conditions

Powered by PhDFocusTM