Numerical Study on the Boundary Value Problem by Using a Shooting Method

Md. Mizanur Rahman; Mst. Jesmin Ara; Md. Nurul Islam; Md. Shajib Ali

doi:doi:10.11648/j.pamj.20150403.16

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Numerical Study on the Boundary Value Problem by Using a Shooting Method

Md. Mizanur Rahman, Mst. Jesmin Ara, Md. Nurul Islam, Md. Shajib Ali

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 3)

Received: 28 April 2015 Accepted: 15 May 2015 Published: 26 May 2015

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Abstract

In the present paper, a shooting method for the numerical solution of nonlinear two-point boundary value problems is analyzed. Dirichlet, Neumann, and Sturm- Liouville boundary conditions are considered and numerical results are obtained. Numerical examples to illustrate the method are presented to verify the effectiveness of the proposed derivations. The solutions are obtained by the proposed method have been compared with the analytical solution available in the literature and the numerical simulation is guarantee the desired accuracy. Finally the results have been shown in graphically.

Published in	Pure and Applied Mathematics Journal (Volume 4, Issue 3)
DOI	10.11648/j.pamj.20150403.16
Page(s)	96-100
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), 2024. Published by Science Publishing Group

Keywords

Boundary Value Problem, Shooting Method, Numerical Simulation and MATLAB Programming

References

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[2]	Huilan Wang, Zigen Ouyang and Liguang Wan, “Application of the shooting method to second – order multi- point integral boundary value problems,” A Spinger open Journal ,Article ID 205, 2013 .
[3]	Man KamKwong and James S. W. Wong, “The shooting method and non-homogeneous multipoint BVPs of second-order ODE,”. Hindawi Publishing Corporation, Article ID 64012, 2007.
[4]	W. M. Abd-Elhameed, E. H. Doha and Y. H. Youssri, “New wavelates collection method for solving second-order multipoint boundary value problems using Chebyshev polynomials of third and fourth kinds,” Hindawi Publishing Corporation, Article ID 542839, 2013.
[5]	Phang Pei See, Zanariah Abdul Majid and Mohamed Suleiman, “Solving nonlinear two point boundary value problem using two step direct method,” Journal of Quality Measurement and Analysis, vol. 7, No. 1, pp. 129-140, 2011.
[6]	Douglas B. Meade, Bala S. Haran and Ralph E. White, “The shooting technique for the solution two-point boundary value problems”, 1996.
[7]	M. M. Rahman, M.A. Hossen, M. Nurul Islamand Md. Shajib Ali, “Numerical Solutions of Second Order Boundary Value Problems by Galerkin Method with Hermite Polynomials,” Annals of Pure and Applied Mathematics Vol. 1, No. 2, pp. 138-148, 2012.
[8]	Afet Golayoglu Fatullayev, Emine Can and CananKoroglu, “Investigated numerical solution of a boundary value problem for a second order Fuzzy differential equation,”. TWMS J. Pure Appl. Math, vol. 4, No. 2, pp. 169-176, 2013.
[9]	A. Granas, R. B. Guenther and J. W. Lee, “The shooting method for the numerical solution of a class of nonlinear boundary value problems,” SIAM J. Numer. Anal., vol. 16, No. 5, pp. 828–836, 2006.
[10]	A. T. Cole and K. R. Adeboye, “Studied an alternative approach to solutions of nolinear two point boundary value problems,” International Journal of Information and Communication Technology Research, vol. 3, No. 4, 2013.
[11]	Tiantian Qiao and Weiguo Li, “Two kinds of important numerical methods forcalculating periodic solutions” Journal of Information and Communication science, vol. 1, pp. 85-92, 2006.
[12]	Nguyen Trung Hieu, “Remarks on the shooting method for nonlinear two-point boundary value problem,” VNU. JOURNAL OF SCIENCE, Mathematics-Physics, 2003.
[13]	R. D. Russell and L. F. Shampine, “Numerical methods for singular boundary value problem,” SIAM. J. Numer. Anal., vol. 12, No. 1, pp. 13-36, 2006.
[14]	Dinkar Sharma, Ram Jiuari and Sheo Kumar, “Numerical solution of two-point boundary value problems using Galerkin-Finite element method.” International Journal of Nonlinear Science, vol. 13, No. 2, pp. 204-210,2012.
[15]	L. F. Shampine, I. Gladwell and S. Thompson. Solving ODEs with MATLAB, 2003.
[16]	L. F. Shampine, J. Kierzenka and M. W. Reichelt, “Solving boundary value problem for ordinary differential equations in MATLAB with bvp4c,” 2000.
[17]	Stephen J. Chapman, MATLAB Programming for Engineers, Thomson Learning, 2004.

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APA Style

Md. Mizanur Rahman, Mst. Jesmin Ara, Md. Nurul Islam, Md. Shajib Ali. (2015). Numerical Study on the Boundary Value Problem by Using a Shooting Method. Pure and Applied Mathematics Journal, 4(3), 96-100. https://doi.org/10.11648/j.pamj.20150403.16

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ACS Style

Md. Mizanur Rahman; Mst. Jesmin Ara; Md. Nurul Islam; Md. Shajib Ali. Numerical Study on the Boundary Value Problem by Using a Shooting Method. Pure Appl. Math. J. 2015, 4(3), 96-100. doi: 10.11648/j.pamj.20150403.16

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AMA Style

Md. Mizanur Rahman, Mst. Jesmin Ara, Md. Nurul Islam, Md. Shajib Ali. Numerical Study on the Boundary Value Problem by Using a Shooting Method. Pure Appl Math J. 2015;4(3):96-100. doi: 10.11648/j.pamj.20150403.16

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@article{10.11648/j.pamj.20150403.16,
  author = {Md. Mizanur Rahman and Mst. Jesmin Ara and Md. Nurul Islam and Md. Shajib Ali},
  title = {Numerical Study on the Boundary Value Problem by Using a Shooting Method},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {3},
  pages = {96-100},
  doi = {10.11648/j.pamj.20150403.16},
  url = {https://doi.org/10.11648/j.pamj.20150403.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150403.16},
  abstract = {In the present paper, a shooting method for the numerical solution of nonlinear two-point boundary value problems is analyzed. Dirichlet, Neumann, and Sturm- Liouville boundary conditions are considered and numerical results are obtained. Numerical examples to illustrate the method are presented to verify the effectiveness of the proposed derivations. The solutions are obtained by the proposed method have been compared with the analytical solution available in the literature and the numerical simulation is guarantee the desired accuracy. Finally the results have been shown in graphically.},
 year = {2015}
}

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TY  - JOUR
T1  - Numerical Study on the Boundary Value Problem by Using a Shooting Method
AU  - Md. Mizanur Rahman
AU  - Mst. Jesmin Ara
AU  - Md. Nurul Islam
AU  - Md. Shajib Ali
Y1  - 2015/05/26
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150403.16
DO  - 10.11648/j.pamj.20150403.16
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 96
EP  - 100
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150403.16
AB  - In the present paper, a shooting method for the numerical solution of nonlinear two-point boundary value problems is analyzed. Dirichlet, Neumann, and Sturm- Liouville boundary conditions are considered and numerical results are obtained. Numerical examples to illustrate the method are presented to verify the effectiveness of the proposed derivations. The solutions are obtained by the proposed method have been compared with the analytical solution available in the literature and the numerical simulation is guarantee the desired accuracy. Finally the results have been shown in graphically.
VL  - 4
IS  - 3
ER  -

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Author Information

Md. Mizanur Rahman

Dept. of Mathematics, Faculty of Applied Science and Technology, Islamic University, Kushtia, Bangladesh
Mst. Jesmin Ara

Department of Political Science, National University, Gazipur, Dhaka, Bangladesh
Md. Nurul Islam

Dept. of Mathematics, Faculty of Applied Science and Technology, Islamic University, Kushtia, Bangladesh
Md. Shajib Ali

Dept. of Mathematics, Faculty of Applied Science and Technology, Islamic University, Kushtia, Bangladesh

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Plain Text BibTeX RIS

APA Style

Md. Mizanur Rahman, Mst. Jesmin Ara, Md. Nurul Islam, Md. Shajib Ali. (2015). Numerical Study on the Boundary Value Problem by Using a Shooting Method. Pure and Applied Mathematics Journal, 4(3), 96-100. https://doi.org/10.11648/j.pamj.20150403.16

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ACS Style

Md. Mizanur Rahman; Mst. Jesmin Ara; Md. Nurul Islam; Md. Shajib Ali. Numerical Study on the Boundary Value Problem by Using a Shooting Method. Pure Appl. Math. J. 2015, 4(3), 96-100. doi: 10.11648/j.pamj.20150403.16

Copy | Download

AMA Style

Md. Mizanur Rahman, Mst. Jesmin Ara, Md. Nurul Islam, Md. Shajib Ali. Numerical Study on the Boundary Value Problem by Using a Shooting Method. Pure Appl Math J. 2015;4(3):96-100. doi: 10.11648/j.pamj.20150403.16

Copy | Download

@article{10.11648/j.pamj.20150403.16,
  author = {Md. Mizanur Rahman and Mst. Jesmin Ara and Md. Nurul Islam and Md. Shajib Ali},
  title = {Numerical Study on the Boundary Value Problem by Using a Shooting Method},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {3},
  pages = {96-100},
  doi = {10.11648/j.pamj.20150403.16},
  url = {https://doi.org/10.11648/j.pamj.20150403.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150403.16},
  abstract = {In the present paper, a shooting method for the numerical solution of nonlinear two-point boundary value problems is analyzed. Dirichlet, Neumann, and Sturm- Liouville boundary conditions are considered and numerical results are obtained. Numerical examples to illustrate the method are presented to verify the effectiveness of the proposed derivations. The solutions are obtained by the proposed method have been compared with the analytical solution available in the literature and the numerical simulation is guarantee the desired accuracy. Finally the results have been shown in graphically.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Numerical Study on the Boundary Value Problem by Using a Shooting Method
AU  - Md. Mizanur Rahman
AU  - Mst. Jesmin Ara
AU  - Md. Nurul Islam
AU  - Md. Shajib Ali
Y1  - 2015/05/26
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150403.16
DO  - 10.11648/j.pamj.20150403.16
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 96
EP  - 100
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150403.16
AB  - In the present paper, a shooting method for the numerical solution of nonlinear two-point boundary value problems is analyzed. Dirichlet, Neumann, and Sturm- Liouville boundary conditions are considered and numerical results are obtained. Numerical examples to illustrate the method are presented to verify the effectiveness of the proposed derivations. The solutions are obtained by the proposed method have been compared with the analytical solution available in the literature and the numerical simulation is guarantee the desired accuracy. Finally the results have been shown in graphically.
VL  - 4
IS  - 3
ER  -

Copy | Download