Adomain Decomposition Method for Direct Integration of Bernoulli Differential Equations
Abstract
We introduce the basic and less known methodology of Adomian Decomposition Method (ADM) for differential equations. We then formulate the method to obtain analytic solutions in a rapidly convergent series to some class of higher order differential equations.The concept of ADM is further applied to various Bernoulli Differential Equations (BDEs) and the results show excellent potentials of applying this method.References
Y. Cherruault, G. Adomian, K. Abbaoui, and R. Rach.(1995) Further remarks on convergencof decomposition method.International Journal of Bio-Medical Computing, 38:89–93.
Holmqmist Sonia,(2007)An Examination of the Effectiveness of the Adomian Decomposition Methodd in Fluid Dynamics Applications. Electronic These and Dessertations 3207.https://Stars.library.ucf.edu/etd/3207
E.U.Agom and F.O.Ogunfiditimi(2015).Adomian Decomposition Method for Bernoulli Differeential Equations.International Journal of Science and Research(IJSR) 1581-1584.
Giblisco,S.(2001) Mathematical and Physical Data Equations and Rules of Thumb.NewYork,McGraw Hill pp.575.
Brunner h (2004) Collocation Method for Volteral Integral and Related Functional Differential Equations.UK Cambridge University Press.pp. 612.
Adomian, G. (1998). Solution of thomas-fermi equation. Applied Mathematics Letter, 11(4), 131-133.
Adomian, G. (1992). Noise term in decomposition solution series. Computer and Mathematics with Application, 24(11), 61-64.
Agom, E. U., & Badmus, A. M. (2015). A concrete Adomian decomposition method for quadratic riccatis differential equations. Pacific Journal of Science and Technology, 16(2), 57-62.
Holmqmist S. (2007). An examination of the effectiveness of the Adomian decomposition method in fluid dynamics applications (Electronic Thesis and Dissertations). Retrieved from https://Stars.library.ucf.edu /etd/3207.
Agom, E. U., & Ogunfiditimi, F.O. (2015). Adomian decomposition method for Bernoulli differential equations. International Journal of Science and Research. 4(12), 1581-1584.
George Adomian. Solving Frontier Problems of Physics Adomian- Decomposition Method. Kluwer Academic,1994
Li, W., and Pang, Yanni. Applications of Adomian Decomposition method to nonlinear systems, Advances in Dierence Equations, 67 (2020). https://doi.org/10.1186/s13662-020-2529-y