Cyclic Operator Decomposition for Solving the Differential Equations

Ivan Gonoskov

Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia.

DOI: 10.4236/apm.2013.31A025                

Abstract

We present an approach how to obtain solutions of arbitrary linear operator equation for unknown functions. The particular solution can be represented by the infinite operator series (Cyclic Operator Decomposition), which acts the generating function. The method allows us to choose the cyclic operators and corresponding generating function selectively, depending on initial problem for analytical or numerical study. Our approach includes, as a particular case, the perturbation theory, but generally does not require inside any small parameters and unperturbed solutions. We demonstrate the applicability of the method to the analysis of several differential equations in mathematical physics, namely, classical oscillator, Schrodinger equation, and wave equation in dispersive medium.

Keywords

Operator Decomposition; Spectral Theory; Propagator

Conflicts of Interest

The authors declare no conflicts of interest.

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