Cyclic Operator Decomposition for Solving the Differential Equations

• 作者: Ivan Gonoskov
• 来源期刊: 理论数学进展(英文)
• 学科: 数学
• 关键词: OPERATOR DECOMPOSITION SPECTRAL Theory PROPAGATOR
• 年，卷（期）: 2013,（1）
• 页码范围: 178-182
• 页数: 5页
• 分类号: O1

摘要

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.