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This paper considers the extension of the Adomian decomposition method (ADM) for solving nonlinear ordinary differential equations of constant coefficients to those equations with variable coefficients. The total derivatives of the nonlinear functions involved in the problem considered were derived in order to obtain the Adomian polynomials for the problems. Numerical experiments show that Adomian decomposition method can be extended as alternative way for finding numerical solutions to ordinary differential equations of variable coefficients. Furthermore, the method is easy with no assumption and it produces accurate results when compared with other methods in literature.

On Adomian decomposition method for solving nonlinear ordinary differential equations of variable coefficients