Elzaki Transform Series Decomposition Method for Solving Bratu Problems

Öz

In this paper, the Elzaki transform series decomposition method is used numerically to solve nonlinear Bratu differential equations. The method combines the Elzaki transform, series expansion and Adomian polynomials, and hence converges absolutely to the exact solution. Additionally, two numerical examples were presented to illustrate the efficacy and dependability of the suggested approach. Applications for the work can be found in mathematics as well as a number of other scientific and engineering disciplines. Calculations were done using maple 2018 software.

Anahtar Kelimeler

• Elzaki transform
• Adomian Polynomials
• Convergence analysis
• Bratu equations
• Approximate solution

Kaynakça

1. [1] Salem, A.S., Thanoon, T.Y., On solving Bratu’s type equation by perturbation Method, Int. J. Nonlinear Anal. Appl, 13(1), 2755-2763, 2022.
2. [2] Zarebnia, M., Hoshyar, M., Solution of Bratu-type equation via spline method, Acta Universities Apulensis, 37, 61–72, 2014.
3. [3] Wazwaz, A.M., The successive differentiation method for solving Bratu equation and Bratu-type equations, Rom. J. Phys, 61, 774–783, 2016.
4. [4] Saravi, M., Hermann M., Kaiser, D., Solution of Bratu’s Equation by He’s variational Iteration Method, Amer. J. Comput. Appl. Math, 3(1), 46–48, 2013.
5. [5] Fenta, H.B., Derese, G.A., Numerical solution of second order initial value problems of Bratu-type equations using sixth order Runge-Kutta seven stages method, Int. J. Comput. Sci. Appl. Math, 5(1), 10-15, 2019.
6. [6] Ezekiel, A., New Improved Variational Homotopy Perturbation Method for Bratu-Type Problems, Amer. J. Comput. Math, 3(2), 110–113, 2013.
7. [7] Hassan, H.N., Semary, M. S., Analytic approximate solution for the Bratu’s problem by optimal homotopy analysis method, Commun. Numerical Anal, 2013, 1-14, 2013.
8. [8] Aregbesola, Y., Numerical solution of Bratu problem using the method of weighted residual, Elect. J. South African Math. Soc, 3(1), 1–7, 2003.

9. [9] Wazwaz, A.M., Adomians decomposition method for a reliable treatment of the Bratu-type equations, Appl. Math. Comput, 166(3), 652–663, 2005.
10. [10] Changqing, Y., Jianhua, H., Chebyshev wavelets method for solving Bratu’s problem, Bound. Value Prob, 2013(142), 1–9, 2013.
11. [11] Aggarwal, S., Mishra, R., Chaudhary, A., A comparative study of Mohand and Elzaki transforms, Global Journal of Engineering Science and Researches, 6(2), 203-213, 2019.
12. [12] Govind, R. N., Updesh, K., Dinesh, V., A Study on Properties and Applications of Elzaki Transformation, IRE Journals, 5(11), 96-100, 2022.
13. [13] Otaide, I. J., Ugbene, I. J., Application of the Taylor Series Technique to the solution of Bratu Problems, FNAS-JMNS, 2(1), 19-26, 2025.
14. [14] Otaide, I. J., Ugbene, I. J., Step-By-Step Application of Shifted Legendre Polynomials on Numerical Assessment of Non-Linear Bratu Differential Equations, Zamfara International Journal of Education (ZIJE), 4(5), 415-420, 2024.
15. [15] Otaide, I. J., and Enyinnaya E.O., Efficient Numerical Method for Generating Closed Form Solution for Nonlinear Bratu Differential Equations, Journal of Natural Sciences and Mathematics Research, 11(2), 136-145, 2025.
16. [16] Alkan, A., Türk, S., Anaç, H., Caputo-Fabrizio Fractional Elzaki Decomposition Technique for Caputo-Fabrizio Fractional Telegraph Equation, International Journal of Advanced Natural Sciences and Engineering, 9(12), 25-33, 2025.