RESUMEN

A wide class of nonlinear equations is studied in the geometrical optics approximation. It is shown that a nonlinear equation with coefficients dependent on the amplitude of the function sought can be reduced to a system of quasi-linear equations of the gas-dynamics type. As an illustration, the Hamilton--Jacobi equation with a specific form of the nonlinear operator has been solved, and the propagation of monochromatic waves and of point source radiation in nonlinear media has been studied.

RESUMEN

A class of Newton-like methods for enclosing solutions of nonlinear equations is considered. Given q Є (1,2], criteria that yield an R-order of convergence of at least q are derived. In particular, it is shown that under certain circumstances this R-order can reach 2. The results are illustrated on a discretized version of Chandrasekhar’s H-equation.