Finite-difference methods for problem of conjugation of hyperbolic and parabolic equations

A problem of conjugation of hyperbolic and parabolic equations in domain wi th moving boundaries is considered. Existence and uniqueness of a strong so lution of the given problem are proved. A priori estimate for operator-diff erence scheme with non-self-adjoint spatial operator is obtain. Homogeneous difference scheme with constant weights for the conjugation problem is con structed. Moreover, consistency conditions are approximated with the second -order of accuracy with respect to spatial variables. Stability and converg ence of the suggested scheme are investigated.