Scientific communications

Explicit method of numerical solution of a problem of light wave propagation in nonlinear media

A. G. Vasil'kov, Yu. K. Danileiko, T. P. Lebedeva, M. F. Romanov

Moscow

Abstract: A method for the numerical solution of problems of the propagation of axially-symmetric beams in media with a positive cubic non-linearity in the framework of a parabolic equation is discussed. For such problems it is established by a numerical experiment that only the use of a moving Lagrangian mesh leads to the stability of explicit methods of numerical solution. The influence of the boundary conditions on the solution of such problems is examined. The scheme proposed can be used for multidimensional problems.

UDC: 519.6:517.958

Received: 28.10.1980
Revised: 23.07.1982

 English version: USSR Computational Mathematics and Mathematical Physics, 1983, 23:3, 146–150

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