EFFECTIVE BOUNDARY CONDITIONS IN THE NUMERICAL SOLUTION OF CAUCHY PROBLEM FOR PARABOLIC EQUATIONS

P. N. Vabishchevich, N. N. Elkin
VANT. Ser. Mat. Mod. Fiz. Proc 1991. Вып.1. С. 54-57.

      When solving numerically the Cauchy problem, the need in setting boundary conditions occurs due to the transition from an unbounded computational domain to the bounded domain. In the present work effective boundary conditions are set for parabolic equations on the basis of the Cauchy problem solution represented using potentials. The integral formulation of the problem outside the computational domain is combined with the differential formulation inside the computational domain. In practice, the approach is based on solving an auxiliary initial boundary value problem with the preset boundary conditions and, then, the boundary conditions for the major problem are calculated.