APPLICATION OF INTEGRAL OPERATORS TO SINGULAR DIFFERENTIAL EQUATIONS AND TO COMPUTATIONS OF COMPRESSIBLE FLUID FLOWS.

Abstract

The application of the method of integral operators in the theory of partial differential equations is discussed. The operators transforming analytic functions f(u) of one variable into solutions of D(psi) = zero and their inverses are described. A survey of results about the theorems which follow by 'transplanting' relations in the theory of analytic functions of one and several variables is presented. Among others, theorems about approximation of a solution by linear combination are discussed. Here psi sub v, v = 1, 2, ... is a set of particular solutions. The construction of the psi sub v and application of this approach to the solution of boundary value problems are presented. The equation arises in the theory of compressible fluids. The constructions of subsonic and transonic flows are described and examples are given. The use of the difference method in connection with the computation of flow patterns using the integral operator method is discussed. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1966
Accession Number
AD0630529

Entities

People

  • Stefan Bergman

Tags

DTIC Thesaurus Topics

  • Analytic Functions
  • Boundary Value Problems
  • Computations
  • Construction
  • Differential Equations
  • Equations
  • Flow
  • Fluid Flow
  • Integrals
  • Partial Differential Equations
  • Transonic Flow

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Linear Algebra

Technology Areas

  • Biotechnology