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首页> 外文期刊>Moscow University Physics Bulletin >A Method of Inverse Differential Operators Using Ortogonal Polynomials and Special Functions for Solving Some Types of Differential Equations and Physical Problems
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A Method of Inverse Differential Operators Using Ortogonal Polynomials and Special Functions for Solving Some Types of Differential Equations and Physical Problems

机译：一种使用正交多项式和特殊函数的微分算子逆方法来求解某些类型的微分方程和物理问题

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摘要

A general operational method, which is based on the developed technique of the inverse derivative operator, for solving a wide range of problems described by some classes of differential equations is represented. The inverse derivative operators for solving a number of differential equations are constructed and used. The operational identities are derived with the use of the inverse derivative operator, integral transformations, and generalized forms of orthogonal polynomials and special functions. Examples of solving various partial differential equations, such as equations of heat conduction and diffusion, as well as the Fokker-Planck equation, etc. are given. The application of the operational approach to solving a number of physical problems, among them problems related to the motion of charged particles in external field, is demonstrated.
机译：提出了一种基于逆导数算子的发展技术的通用运算方法，用于解决由某些类型的微分方程描述的各种问题。构造并使用了用于求解许多微分方程的逆导数算子。通过使用逆导数运算符，积分变换以及正交多项式和特殊函数的广义形式来导出操作标识。给出了求解各种偏微分方程的例子，例如热传导和扩散方程，以及Fokker-Planck方程等。演示了操作方法在解决许多物理问题中的应用，其中包括与带电粒子在外场中运动有关的问题。

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