Improved structural methods for nonlinear differential-algebraic equations via combinatorial relaxation

Abstract Differential-algebraic equations (DAEs) are widely used for modelling dynamical systems. In the numerical analysis of DAEs, consistent initialization and index reduction important preprocessing steps prior to integration. Existing DAE solvers commonly adopt structural methods based on combinatorial optimization. Unfortunately, fail if has a singular system Jacobian matrix. For such have been proposed modify them other DAEs which applicable, relaxation technique. modification methods, however, work only that linear or close linear. This paper presents two new nonlinear DAEs: substitution method augmentation method. Both approach applicable large class DAEs. The symbolically solves some derivatives implicit function theorem substitutes solution back into system. Instead solving equations, modifies by appending variables equations. Our implemented as MATLAB library using MuPAD, through its application practical we show our can be promising procedure in cannot handle.