Adomian’s decomposition method

Approximate Analytical Solutions for Models of Three-Dimensional Electrodes by Adomian s Decomposition Method... 

Adomian s Decomposition Method is used to solve the model equations that are in the form of nonlinear differential equation(s) with boundary conditions.2,3 Approximate analytical solutions of the models are obtained. The approximate solutions are in the forms of algebraic expressions of infinite power series. In terms of the nonlinearities of the models, the first three to seven terms of the series are generally sufficient to meet the accuracy required in engineering applications. 

Scott K, Sun Y-P (2007) Approximate analytical solutions for models of three-dimensional electrodes by Adomian s decomposition method. In Vayenas C, White R, Gamboa-Aldeco ME (eds) Modem aspects of electrochemistry 41. Springer, New York, pp 221-304... 

G. 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... 

The model solution of porous or particulate three-dimensional electrodes is obtained using the Adomian s inverse operator method (IOM) or Decomposition Method . Data calculated by the decomposition method, are comparable with that obtained by a finite difference method using the BAND program. In general the Adomian method gives faster convergence, than that of the finite difference method, for the model over a wide range of parameters. 

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