The decomposition method for nonlinear dynamical systems
After asserting that all real problems are nonlinear, often strongly nonlinear, the author goes into considerations about deviations of the solutions from the actual physical behavior. He then introduces a decomposition method, of an operator-theoretic approach, in which general dynamical systems are viewed as being nonlinear and stochastic and described by nonlinear stochastic differential equations, systems of equations or partial differential equations. The method consists essentially in decomposing the solution process into additive components, the first being the solution of a simplified linear deterministic system and which takes into account the initial conditions, and each of the subsequent components is found in terms of a preceding one, thus ultimately in terms of the first. Several examples are given.
scientific article; zbMATH DE number 4015235
scientific article