Influence of complex coefficients on the stability of difference scheme for parabolic equations with non-local conditions

The stability of a finite difference scheme for Schrödinger, Kuramoto-Tsuzuki and parabolic equations, subject to non-local conditions with complex coefficients, is dealt with. The stability conditions, which have to be met by complex coefficients in non-local conditions, have been determined. The main result of this study is that complex coefficients together with non-local conditions cause new effects on the stability of difference scheme. Numerical experiment has revealed additional regularities in the stability conditions.