Accession Number : AD0784394

Title :   Numerical Calculation of Non-Unique Solutions of a 2D Sinh-Poisson Equation.

Descriptive Note : Interim rept.,


Personal Author(s) : McDonald,B. E.

Report Date : JUL 1974

Pagination or Media Count : 22

Abstract : The author gives a method for computing non-trivial solutions to the nonlinear partial differential equation (del squared)psi + (lambda squared) sinh psi = O, with psi = O on a square boundary. The method consists of a Newton-Raphson iteration, in which successive corrections to psi must satisfy a linearized partial differential equation. The author gives a direct solution algorithm for the linearized equation, which is suitable for small meshes. Using this method, the author establishes the non-uniqueness of solutions by finding six solutions for the same value of lambda. Calculation of these solutions required from 4 to about 40 iterations each, depending upon the accuracy of the initial approximation. (Modified author abstract)

Descriptors :   *Plasmas(Physics), *Waveguides, *Partial differential equations, Statistical mechanics, Nonlinear differential equations, Potential theory, Numerical analysis

Subject Categories : Plasma Physics and Magnetohydrodynamics

Distribution Statement : APPROVED FOR PUBLIC RELEASE