Adomians Decomposition Method ADM

Adomian developed the decomposition method to solve the deterministic or stochastic differential equations.3 The solutions obtained are approximate and fast to converge, as shown by Cherrault.8 In general, satisfactory results can be obtained by using the first few terms of the approximate, series solution. According to Adomian s theory, his polynomials can approximate the 

In general a differential equation can be expressed by an operator equation.3,9 With the first decomposition, the original deterministic non-linear differential equation can be written in the Adomian s general form as  

Furthermore the decomposition method identifies the nonlinear term by the decomposition series 

Other polynomials can be generated in a similar manner.. 1, depends only on 0, Ax depends only on n0 and uu A2 depends only on u(h u, and u2, and so on. It is clear that A, is always determined 

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The solution method, the Adomian Decomposition Method (ADM), is mechanized for solving the nonlinear models according to the principle of Parameter Decomposition .2,3 A Mathematica code of the ADM,12 for general order reactions in planar or spherical catalyst pellets, is given in more detail in the Appendix. Thus, the algebraic expressions of the approximate solutions and the computed data of results can all be easily obtained. 

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