RP-Department of Mathematics
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Browsing RP-Department of Mathematics by Subject "Adomian decomposition method"
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Item Adomian Decomposition Method On Nonlinear Singular Cauchy Problem of Euler-Poisson- Darbuox equation(Islamic Azad University, Rasht Branch, 2010) Iyaya, Wanjala C. C.In this paper, we apply Picard’s Iteration Method followed by Adomian Decomposition Method to solve a nonlinear Singular Cauchy Problem of Euler- Poisson- Darboux Equation. The solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by Carroll and Showalter (1976)in the solution of Singular Cauchy Problem.Item Modelling childhood disease outbreak in a community with inflow of susceptible and vaccinated new-born(Research India Publications, 2016) Yano, T.P.; Oluwole, D.M.; Malonza, D.M.This paper investigates the transmission dynamics of a Childhood disease outbreak in a community with direct inflow of susceptible and vaccinated new-born. Qualitative analysis of the SEIR nonlinear model is performed for disease free and endemic equilibria using the stability theory of differential equations. The disease free state is found to be both locally and globally asymptotically stable when the vaccination reproductive number v R is less than unity. In addition, the model exhibits transcritical forward bifurcation phenomenon and the sensitivity indices of the vaccination reproductive number with respect to various model parameters is determined. Using the Adomian decomposition method (ADM) and the fourth order Runge-Kutta integration scheme (RK4), the semi-analytical and numerical solutions of the nonlinear model are obtained. Pertinent results are displayed graphically and in tabular form. A vaccination coverage threshold is obtained above which the disease will be effectively eliminated from the community.