APPLICATION OF INTEGRAL OPERATORS TO SINGULAR DIFFERENTIAL EQUATIONS AND TO COMPUTATIONS OF COMPRESSIBLE FLUID FLOWS.
Technical summary rept.,
MATHEMATICS RESEARCH CENTER UNIV OF WISCONSIN MADISON
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The application of the method of integral operators in the theory of partial differential equations is discussed. The operators transforming analytic functions fu of one variable into solutions of Dpsi 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
- Numerical Mathematics
- Fluid Mechanics