A Galerkin Finite Element Method for Two-Point Boundary Value Problems of Ordinary Differential Equations

Gentian Zavalani

doi:doi:10.11648/j.acm.20150402.15

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A Galerkin Finite Element Method for Two-Point Boundary Value Problems of Ordinary Differential Equations

Gentian Zavalani

Published in Applied and Computational Mathematics (Volume 4, Issue 2)

Received: 26 February 2015 Accepted: 16 March 2015 Published: 21 March 2015

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Abstract

In this paper, we present a new method for solving two-point boundary value problem for certain ordinary differential equation. The two point boundary value problems have great importance in chemical engineering, deflection of beams etc. In this study, Galerkin finite element method is developed for inhomogeneous second-order ordinary differential equations. Several examples are solved to demonstrate the application of the finite element method. It is shown that the finite element method is simple, accurate and well behaved in the presence of singularities.

Published in	Applied and Computational Mathematics (Volume 4, Issue 2)
DOI	10.11648/j.acm.20150402.15
Page(s)	64-68
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Exact Solution, Two-Point Value Boundary Problem, Finite Element Method

References

[1]	C.w. Cryer, The numerical solution of boundary value problems for second order functional differential equations by finite differences, Numer. Math. 20 (1973) 288-299.
[2]	Y.F. Holt, Numerical solution of nonlinear two-point boundary value problems by finite difference method, Comm. ACM 7 (1964) 363-373.
[3]	P.G. Ciarlet, M.H. Schultz and R.S. Varga, Numerical methods of high order accuracy for nonlinear boundary value problems, Numer. Math. 13 (1967) 51-77.
[4]	S Arora, S S Dhaliwal, V K Kukreja. Solution of two point boundary value problems using orthogonal collocation on finite elements. Appl. Math. Comput., 171(2005):358-370.
[5]	J Villadsen, W E Stewart. Solution of boundary value problems by orthogonal collocation. Chem. Eng. Sci., 22(1967): 1483-1501.
[6]	B Jang. Two-point boundary value problems by the extended Adomian decomposition method. J. Comput. Appl.Math., 219 (1)(2008): 253-262.
[7]	A Dogan. A Galerkin finite element approach of Burgers’ equation. Appl. Math. Comput., 157 (2)(2004): 331-346.
[8]	T K Sengupta, S B Talla, S C Pradhan. Galerkin finite element methods for wave problems. Sadhana, 30 (5)(2005): 611-623.
[9]	H Kaneko, K S Bey, G J W Hou. Discontinuous Galerkin finite element method for parabolic problems. Appl. Math. Comput., 182 (1)(2006):388-402.
[10]	M A EI-Gebeily, K M Furati, D O’Regan. The finite element-Galerkin method for singular self-adjoint differential equations. J. Comput. Appl. Math., 223 (2)(2009): 735-752.
[11]	D Sharma, R Jiwari, S Kumar. Galerkin-finite Element Methods for Numerical Solution of Advection- Diffusion Equation. Int. J. Pure and Appl. Math., 70 (3)(2011): 389-399.
[12]	S E Onath. Asymptotic behavior of the Galerkin and the finite element collocation methods for a parabolic equation. Appl. Math. Comput., 127(2002):207-213.
[13]	T Jangveladze, Z Kiguradze, B Neta. Galerkin finite element method for one nonlinear integro-differential model. Appl. Math. Comput., 217 (16)(2011):6883-6892.

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Gentian Zavalani. (2015). A Galerkin Finite Element Method for Two-Point Boundary Value Problems of Ordinary Differential Equations. Applied and Computational Mathematics, 4(2), 64-68. https://doi.org/10.11648/j.acm.20150402.15

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ACS Style

Gentian Zavalani. A Galerkin Finite Element Method for Two-Point Boundary Value Problems of Ordinary Differential Equations. Appl. Comput. Math. 2015, 4(2), 64-68. doi: 10.11648/j.acm.20150402.15

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AMA Style

Gentian Zavalani. A Galerkin Finite Element Method for Two-Point Boundary Value Problems of Ordinary Differential Equations. Appl Comput Math. 2015;4(2):64-68. doi: 10.11648/j.acm.20150402.15

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  author = {Gentian Zavalani},
  title = {A Galerkin Finite Element Method for Two-Point Boundary Value Problems of Ordinary Differential Equations},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {2},
  pages = {64-68},
  doi = {10.11648/j.acm.20150402.15},
  url = {https://doi.org/10.11648/j.acm.20150402.15},
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  abstract = {In this paper, we present a new method for solving two-point boundary value problem for certain ordinary differential equation. The two point boundary value problems have great importance in chemical engineering, deflection of beams etc. In this study, Galerkin finite element method is developed for inhomogeneous second-order ordinary differential equations. Several examples are solved to demonstrate the application of the finite element method. It is shown that the finite element method is simple, accurate and well behaved in the presence of singularities.},
 year = {2015}
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TY  - JOUR
T1  - A Galerkin Finite Element Method for Two-Point Boundary Value Problems of Ordinary Differential Equations
AU  - Gentian Zavalani
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Author Information

Gentian Zavalani

Faculty of Mathematics and Physics Engineering Polytechnic University of Tirana, Albania

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APA Style

Gentian Zavalani. (2015). A Galerkin Finite Element Method for Two-Point Boundary Value Problems of Ordinary Differential Equations. Applied and Computational Mathematics, 4(2), 64-68. https://doi.org/10.11648/j.acm.20150402.15

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ACS Style

Gentian Zavalani. A Galerkin Finite Element Method for Two-Point Boundary Value Problems of Ordinary Differential Equations. Appl. Comput. Math. 2015, 4(2), 64-68. doi: 10.11648/j.acm.20150402.15

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AMA Style

Gentian Zavalani. A Galerkin Finite Element Method for Two-Point Boundary Value Problems of Ordinary Differential Equations. Appl Comput Math. 2015;4(2):64-68. doi: 10.11648/j.acm.20150402.15

Copy | Download

@article{10.11648/j.acm.20150402.15,
  author = {Gentian Zavalani},
  title = {A Galerkin Finite Element Method for Two-Point Boundary Value Problems of Ordinary Differential Equations},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {2},
  pages = {64-68},
  doi = {10.11648/j.acm.20150402.15},
  url = {https://doi.org/10.11648/j.acm.20150402.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150402.15},
  abstract = {In this paper, we present a new method for solving two-point boundary value problem for certain ordinary differential equation. The two point boundary value problems have great importance in chemical engineering, deflection of beams etc. In this study, Galerkin finite element method is developed for inhomogeneous second-order ordinary differential equations. Several examples are solved to demonstrate the application of the finite element method. It is shown that the finite element method is simple, accurate and well behaved in the presence of singularities.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - A Galerkin Finite Element Method for Two-Point Boundary Value Problems of Ordinary Differential Equations
AU  - Gentian Zavalani
Y1  - 2015/03/21
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150402.15
DO  - 10.11648/j.acm.20150402.15
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 64
EP  - 68
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150402.15
AB  - In this paper, we present a new method for solving two-point boundary value problem for certain ordinary differential equation. The two point boundary value problems have great importance in chemical engineering, deflection of beams etc. In this study, Galerkin finite element method is developed for inhomogeneous second-order ordinary differential equations. Several examples are solved to demonstrate the application of the finite element method. It is shown that the finite element method is simple, accurate and well behaved in the presence of singularities.
VL  - 4
IS  - 2
ER  -

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