Structural analysis of integro-differential-algebraic equations

We describe a method for analyzing the structure of a system of nonlinear integro-differential-algebraic equations (IDAEs) that generalizes the Sigma-method for the structural analysis of differential-algebraic equations. The method is based on the sparsity pattern of the IDAE and the nu-smoothing property of a Volterra integral operator. It determines which equations and how many times they need to be differentiated to determine the index, and it reveals the hidden constraints and compatibility conditions in order to prove the existence of a solution. The success of the Sigma-method is indicated by the non-singularity of a certain Jacobian matrix. Although it is likely the Sigma-method can be directly applied with success to many problems of practical interest, it can fail on some solvable IDAEs. Accordingly, we also present two techniques for addressing these failures. (C) 2021 Elsevier B.V. All rights reserved.