A modified collocation method for solving differential-algebraic equations

摘要

In this study, a modified collocation method is introduced for solving nonlinear initial value problems and their sensitivity profiles of mixed differential and algebraic equations. The weighted residual equation in the modified method is defined based on the integral expression of the problem. The additional equality constraints for enforcing continuity of the solution at each element boundary are noticeably not required in this study. As a result, the collocation equations in global and finite element time domain are able to unify into a compact formula so that coefficients of the solutions to differential-algebraic equations can be obtained, element by element. The proposed method can be straightforwardly applied for handling sensitivity matrix equations of differential-algebraic problems. The solution and sensitivity profiles of the differential-algebraic equations are simultaneously evaluated by this approach.