
Accession Number : AD0784394
Title : Numerical Calculation of NonUnique Solutions of a 2D SinhPoisson Equation.
Descriptive Note : Interim rept.,
Corporate Author : NAVAL RESEARCH LAB WASHINGTON D C
Personal Author(s) : McDonald,B. E.
Report Date : JUL 1974
Pagination or Media Count : 22
Abstract : The author gives a method for computing nontrivial 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 NewtonRaphson 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 nonuniqueness 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