Research Article

Numerical Solution of Bratu-type Equations by the Variational Iteration Method

Volume: 39 Number: 1 January 1, 2010
  • B. Batiha
TR EN

Numerical Solution of Bratu-type Equations by the Variational Iteration Method

Abstract

In this paper, the variational iteration method (VIM) is applied to obtain approximate analytical solution of Bratu-type equations without any discretization. Comparisons with the exact solutions reveal that VIM is very effective and convenient.

Keywords

References

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  3. Aregbesola, Y. Numerical solution of Bratu problem using the method of weighted residual, Electronic Journal of Southern African Mathematical Sciences Association 3 (01), 1–7, 2003. [4] Ascher, U. M., Matheij, R. and Russell, R. D. Numerical solution of boundary value problems for ordinary differential equations(SIAM, Philadelphia, PA, 1995).
  4. Batiha, B., Noorani, M. S. M. and Hashim, I. Application of variational iteration method to the generalized Burgers-Huxley equation, Chaos Solitons and Fractals 36 (3), 660-ˆu663, 2008.
  5. Batiha, B., Noorani, M. S. M. and Hashim, I. Numerical simulation of the generalized Huxley equation by He’s variational iteration method, Appl. Math. Comput. 186, 1322–1325, 2007. [7] Bildik, N. and Konuralp, A. The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations, Int. J. Nonlinear. Sci. Numer. Simul. 7, 65–70, 2006.
  6. Boyd, J. P. An analytical and numerical study of the two-dimensional Bratu equation, J.Scien. Computing 1 (2), 183–206, 1986.
  7. Boyd, J. P. Chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one-dimensional Bratu equation, Appl. Math. Comput. 142, 189–200, 2003. [10] Chang, S. H. and Chang, transform nonlinear Appl. differential
  8. doi:10.1016/j.amc.2007.05.026. functions, Math. Comput.

Details

Primary Language

English

Subjects

Statistics

Journal Section

Research Article

Authors

B. Batiha This is me

Publication Date

January 1, 2010

Submission Date

May 12, 2014

Acceptance Date

-

Published in Issue

Year 2010 Volume: 39 Number: 1

APA
Batiha, B. (2010). Numerical Solution of Bratu-type Equations by the Variational Iteration Method. Hacettepe Journal of Mathematics and Statistics, 39(1), 23-29. https://izlik.org/JA89RM62WN
AMA
1.Batiha B. Numerical Solution of Bratu-type Equations by the Variational Iteration Method. Hacettepe Journal of Mathematics and Statistics. 2010;39(1):23-29. https://izlik.org/JA89RM62WN
Chicago
Batiha, B. 2010. “Numerical Solution of Bratu-Type Equations by the Variational Iteration Method”. Hacettepe Journal of Mathematics and Statistics 39 (1): 23-29. https://izlik.org/JA89RM62WN.
EndNote
Batiha B (January 1, 2010) Numerical Solution of Bratu-type Equations by the Variational Iteration Method. Hacettepe Journal of Mathematics and Statistics 39 1 23–29.
IEEE
[1]B. Batiha, “Numerical Solution of Bratu-type Equations by the Variational Iteration Method”, Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 1, pp. 23–29, Jan. 2010, [Online]. Available: https://izlik.org/JA89RM62WN
ISNAD
Batiha, B. “Numerical Solution of Bratu-Type Equations by the Variational Iteration Method”. Hacettepe Journal of Mathematics and Statistics 39/1 (January 1, 2010): 23-29. https://izlik.org/JA89RM62WN.
JAMA
1.Batiha B. Numerical Solution of Bratu-type Equations by the Variational Iteration Method. Hacettepe Journal of Mathematics and Statistics. 2010;39:23–29.
MLA
Batiha, B. “Numerical Solution of Bratu-Type Equations by the Variational Iteration Method”. Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 1, Jan. 2010, pp. 23-29, https://izlik.org/JA89RM62WN.
Vancouver
1.B. Batiha. Numerical Solution of Bratu-type Equations by the Variational Iteration Method. Hacettepe Journal of Mathematics and Statistics [Internet]. 2010 Jan. 1;39(1):23-9. Available from: https://izlik.org/JA89RM62WN