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Article History JEL Classification:65L05, 65L06, 65L07, 65D20.In this paper, we show the parallel of Adomian Decomposition Method (ADM) and Lobatto-Runge-Kutta Collocation Method (LRKCM) on first order initial value stiff differential equations. The former method provided closed form solutions while the latter gave approximate solutions. We illustrated these findings in two numerical examples. ADM solutions were in series form while those of LRKCM gave sizeable absolute error. We further visualized our findings in respective plots to show the great potentials of ADM over LRKCM in providing analytical solutions to stiff differential equations.Contribution/Originality: This study contributes in showing the originality of ADM in obtaining exact solution to Stiff differential equations, while LRKCM provided approximate solution whose accuracy depended on step size.

In this paper, Cubic B-Spline collocation method (CBSCM) and Adomian Decomposition Method (ADM) are applied to obtain numerical solutions to fourth-order linear and nonlinear differential equations. The CBSCM was based on finite element method involving collocation method with cubic B-spline as a basis function. While ADM was based on multistage decomposition method. We discovered in the illustrative examples considered, that result by ADM were compatible with the closed form solutions well over twenty, in some cases over thirty, decimal places and with extremely minimal absolute errors. Results by CBSCM gave correct solutions to atmost six decimal places with sizeable absolute errors. These has further revealed the importance and superiority of ADM over CBSCM in providing semi-analytic solution to this class of differential equations.

Article History KeywordsAdomian polynomials Adomian decomposition method Lane-Emden.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.Contribution/ Originality: 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.