ALGEBRAIC COMPUTATION AND THE DECOMPOSITION METHOD

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Abstract
The decomposition method of Adomian, which was developed to solve nonlinear stochastic differential equations, has recently been generalized in a number of directions and is now applicable to wide classes of linear and nonlinear, deterministic and stochastic differential, partial differential, and differential delay equations as well as algebraic equations of all types including polynomial equations, matrix equations, equations with negative or nonintegral powers, and random algebraic equations. This paper will demonstrate applicability to transcendental equations as well. The decomposition method basically considers operator equations of the form Fu = g where g may be a number, a function, or even a stochastic process. F is an operator which in general is nonlinear. (If it involves stochastic processes as well, we use a script letter F). The operator F may be a differential or algebraic operator. In this paper we will concentrate on the latter. The authors have thus developed a useful system for realistic solutions of real‐world problems.

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