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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• 作者：K. V. Zhukovsky
• 关键词：inverse operator ; inverse derivative ; exponential operator ; differential equation ; Laguerre and Hermite polynomials ; special functions
• 刊名：Moscow University Physics Bulletin
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：70
• 期：2
• 页码：93-100
• 全文大小：195 KB
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• 作者单位：K. V. Zhukovsky (1)
  
  1. Department of Physics, Moscow State University, Moscow, 119991, Russia
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Russian Library of Science
  
• 出版者：Allerton Press, Inc. distributed exclusively by Springer Science+Business Media LLC
• ISSN：1934-8460

文摘

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.