An efficient algorithm for the solution of a coupled Sylvester equation appearing in descriptor systems

Descriptor systems consisting of a large number of differential–algebraic equations (DAEs) usually arise from the discretization of partial differential–algebraic equations. This paper presents an efficient algorithm for solving the coupled Sylvester equation that arises in converting a system of linear DAEs to ordinary differential equations. A significant computational advantage is obtained by exploiting the structure of the involved matrices. The proposed algorithm removes the need to solve a standard Sylvester equation or to invert a matrix. The improved performance of this new method over existing techniques is demonstrated by comparing the number of floating-point operations and via numerical examples.