Application of the Taylor Series Technique to the Solution of Bratu Problems
Keywords:
Non-linear differential equations, Taylor series, Bratu equations, Approximate solutionAbstract
This study presents a numerical solution of the Bratu differential equations (BDE) using Taylor’s series technique. The effectiveness and reliability of the proposed method were further demonstrated by two numerical examples. The outcomes were also compared to other previously published research. Our suggested approach outperforms the Salem and Thanoon (2022) method in terms of approximating the exact solution. The Maple 18 software was used to perform the computations.
References
Problems
26 Cite this article as:
Otaide, I.J., & Ugbene I.J. (2025). Application of the Taylor series technique to the solution of Bratu problems. FNAS
Journal of Mathematical Modeling and Numerical Simulation, 2(2), 19-26.
References
Aregbesola, Y. (2003). Numerical solution of Bratu problem using the method of weighted residual, Elect. J. South African Math. Soc., 3(1), 1–7.
Changqing, Y., & Jianhua H. (2013). Chebyshev wavelets method for solving Bratu’s problem, Bound. Value Prob.(1), 1–9.
Ezekiel A. (2013). New Improved Variational Homotopy Perturbation Method for Bratu-Type Problems, Amer. J. Comput. Math., 3(2),110–113.
Fenta, H. B., & Derese G. A. (2019). 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),
Hassan, H. N., & Semary, M. S. (2013). Analytic approximate solution for the Bratu’s problem by optimal homotopy analysis method, Commun. Numerical Anal, 1-14.
Otaide I. J., & Oluwayemi M. O. (2024). Numerical treatment of linear volterra integro differential equations using variational iteration algorithm with collocation, Partial Differential Equations and Applied Mathematics, doi: https://doi.org/10.1016/j.padiff.2024.100693.
Oyedepo, T., Oluwayemi, M. O., Ayinde, M. A., Osilagun, J. A., &Ahmed L. O. (2023). Homotopy Perturbation Technique for Fractional Volterra and Fredholm Integro Differential Equations,"International Conference on Science, Engineering and Business for Sustainable Development Goals (SEB-SDG), Omu-Aran, Nigeria,1-6, https://doi.org/10.1109/SEB-SDG57117.2023.10124633. Salem, S. A., & Thanoon, T. Y. (2022). On solving Bratu’s type equation by perturbation method. International Journal of Nonlinear Analysis and Applications, 13(1), 2755-2763.
Saravi, M., Hermann, M., & Kaiser, D. (2013). Solution of Bratu’s Equation by He’s variational Iteration Method, Amer. J. Comput. Appl. Math, 3(1), 46–48.
Wazwaz, A. M. (2005). Adomians decomposition method for a reliable treatment of the Bratu-type equations, Appl. Math. Comput., 166, 652–663.
Wazwaz, A. M. (2016). The successive differentiation method for solving Bratu equation and Bratu-type equations, Rom. J. Phys., 61, 774–783.
Zarebnia M., & Hoshyar M. (2014). Solution of Bratu-type equation via spline method, Acta Universities Apulensis, 37, 61–72.
