Numerical Calculation of Non-Unique Solutions of a 2D Sinh-Poisson Equation.
NAVAL RESEARCH LAB WASHINGTON D C
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The author gives a method for computing non-trivial solutions to the nonlinear partial differential equation del squaredpsi 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
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