A global method for solution of complex systems. (English) Zbl 0556.93005

This paper is intended as a tutorial paper for a general scientific audience to introduce to users a unique methodology for accurately and realistically solving dynamical systems which may be strongly nonlinear and involve stochastic processes in inputs, coefficients, or initial or boundary conditions and special cases such as linear, weakly nonlinear, deterministic, etc., as well. It has distinct advantages over perturbative or hierarchy methods and methods of numerical analysis and is applicable to algebraic equations (polynomial, transcendental, matrix), differential equations, systems of coupled (nonlinear and/or stochastic) differential equations, and (nonlinear and/or stochastic) partial differential equations. Because the methods are applicable to a very wide class of problems in physics, economics, biology and medicine, engineering and technology, the presentation is intended to be accessible to all rather than for applied mathematicians only.


93A99 General systems theory
68U20 Simulation (MSC2010)
93C10 Nonlinear systems in control theory
93E03 Stochastic systems in control theory (general)
Full Text: DOI