Numerical Calculation of Non-Unique Solutions of a 2D Sinh-Poisson Equation.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1974
- Accession Number
- AD0784394
Entities
People
- B. E. Mcdonald
Organizations
- United States Naval Research Laboratory