Numerical Methods for Stiff and Quadratic Differential Equations and For Josephson Equations.

摘要

Stability results for one-leg methods, valid for linear variable coefficient equations and certain nonlinear systems, and for arbitrary variable integration steps, were gotten by linear and nonlinear contractivity analysis. Nonlinear A- and A(alpha)-stability results for multistep methods were obtained by Fourier transform methods. Numerical and analytic results were given for solutions of the equations governing extended Josephson junctions or two-junction interferometers. Special methods were derived for solving quadratic systems of differential equations. (Author)