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On Adomian Polynomials and its Applications to Lane-Emden Type of Equation
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(2017). On Adomian Polynomials and its Applications to Lane-Emden Type of Equation. International Journal of Mathematical Research, 6(1): 13-21. DOI: 10.18488/journal.24.2017.61.13.21
In this paper, we generate the Adomian polynomial for major nonlinear terms which are mostly common in differential equations. And we applied it to Lane-Emden type of equations whose nonlinear terms are exponential functions. The result we obtained by modified Adomian decomposition method (ADM) gave a series solution which is the same as the Taylors series of the exact solution.
This study contributes in the existing literature on the use of Adomian decomposition method. It explicitly provide the Adomian polynomials of frequently occurring nonlinear terms in a linear functional. And, for the first time, applied to obtain an exact solution to the Lane-Emden type of equation.
Analysis of an Eco-Epidemiological Model with Disease in the Prey and Predator
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We analyze and formulate an Eco-Epidemiological model with disease in the prey and predator, study the existence of the non-negative equilibria, obtain the sufficient conditions of locally asymptotical stability of the equilibria, then analyze the global stability of the positive equilibria.
This study contributes in the existing literature of Eco-Epidemiological model. We get the conditions of local asymptotic and the existence of the boundary balance, and we proved the positive balance point is global asymptotical stability by constructing Liapunov function.