Improvement of convergence and numerical stability of the correcting function method for the dynamic problem of a solid body with cavities partially filled by liquid

Method of the convergence and numerical stability improvement based on the correcting potential extension on auxiliary surface adding the moistened vessel surface up to the closed one, is presented. For doublecoupling cavities the method is proposed to extend the basic potential on a fictitious free surface. Continuation of the correcting and basis potentials permits to obtain the more stable algorithms, besides that to extent a possibility of the correcting function method and to propose a new way of coordinate function construction for the variation method. As a model of the cavity formed by excentric spherical and ellipsoidal surfaces, the efficiency of proposed method is shown.