Back
 AJCM  Vol.4 No.2 , March 2014
Numerical solutions of second order initial value problems of Bratu-type via optimal homotopy asymptotic method
Abstract: We present the optimal homotopy asymptotic method (OHAM) to find the numerical solution of the second order initial value problems of Bratu-type. We solve some examples to illustrate the validity and efficiency of the method.
Cite this paper: Darwish, M. and Kashkari, B. (2014) Numerical solutions of second order initial value problems of Bratu-type via optimal homotopy asymptotic method. American Journal of Computational Mathematics, 4, 47-54. doi: 10.4236/ajcm.2014.42005.
References

[1]   Herisanu, N., Marinca, V., Dordea T. and Madescu, G. (2008) A New Analytical Approach to Nonlinear Vibration of an Electrical Machine. Proceedings of the Romanian Academy, Series A, 9, 229-236.

[2]   Ali, J., Islam, S., Islam, S. and Zamand, G. (2010) The Solution of Multipoint Boundary Value Problems by the Optimal Homotopy Asymptotic Method. Computers & Mathematics with Applications, 59, 2000-2006.
http://dx.doi.org/10.1016/j.camwa.2009.12.002

[3]   Ene, R.D., Marinca, V., Negrea, R. and Caruntu, B. (2012) Optimal Homotopy Asymptotic Method for Solving a Nonlinear Problem in Elasticity. Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 14th International Symposium, Timisoara, 26-29 September 2012, 98-102.

[4]   Esmaeilpour, M. and Ganji, D.D. (2010) Solution of the Jeffery-Hamel Flow Problem by Optimal Homotopy Asymptotic Method. Computers & Mathematics with Applications, 59, 3405-3411.
http://dx.doi.org/10.1016/j.camwa.2010.03.024

[5]   Hashmi, M.S., Khan, N. and Iqbal, S. (2012) Optimal Homotopy Asymptotic Method for Solving Nonlinear Fredholm Integral Equations of Second Kind. Applied Mathematics and Computation, 218, 10982-10989.
http://dx.doi.org/10.1016/j.amc.2012.04.059

[6]   Marinca, V., Herisanu, N., Bota, C. and Marinca, B. (2009) An Optimal Homotopy Asymptotic Method Applied to the Steady Flow of a Fourth-Grade Fluid Past a Porous Plate. Applied Mathematics Letters, 22, 245-251.
http://dx.doi.org/10.1016/j.aml.2008.03.019

[7]   Abukhaled, M., Khuri, S. and Sayfy, A. (2012) Spline-Based Numerical Treatments of Bratu-Type Equations. Palestine Journal of Mathematics, 1, 63-70.

[8]   Wazwaz, A. (2012) A Reliable Study for Extensions of the Bratu Problem with Boundary Conditions. Mathematical Methods in the Applied Sciences, 35, 845-856. http://dx.doi.org/10.1002/mma.1616

[9]   Batiha, B. (2010) Numerical Solution of Bratu-Type Equations by the Variational Iteration Method. Hacettepe Journal of Mathematics and Statistics, 39, 23-29.

[10]   Feng, X., He, Y. and Meng, J. (2008) Application of Homotopy Perturbation Method to the Bratu-Type Equations. Topological Methods in Nonlinear Analysis, 31, 243-252.

[11]   Rashidinia, J., Maleknejad, K. and Taheri, N. (2013) Sinc-Galerkin Method for Numerical Solution of the Bratu’s Problems. Numerical Algorithms, 62, 1-11. http://dx.doi.org/10.1007/s11075-012-9560-3

[12]   Syam, M.I. and Hamdan, A. (2006) An Efficient Method for Solving Bratu Equations. Applied Mathematics and Computation, 176, 704-713. http://dx.doi.org/10.1016/j.amc.2005.10.021

[13]   Wazwaz, A. (2005) Adomian Decomposition Method for a Reliable Treatment of the Bratu-Type Equations. Applied Mathematics and Computation, 166, 652-663. http://dx.doi.org/10.1016/j.amc.2004.06.059

 
 
Top