Decoupling of general integro-differential-algebraic equations into a regular system: Numerical treatment

Similar to differential-algebraic equations (DAEs), the concept of the index is the key to the theoretical and numerical analysis of the integro-differential-algebraic equations (IDAEs). In this paper, we define the tractability index for IDAEs by considering the υ-smoothing property of Volterra integral operator. Using the concept of tractability index, the general form of IDAEs is decoupled into the inherent mixed system of regular second-kind Volterra integrodifferential equations and first-kind integral equations. A numerical method is suggested for solving the obtained problem and convergence analysis is investigated. Some test problems are considered for showing efficiency of the method.