A new procedure for solving differential-algebraic equations

In this article a new algorithm for solving differential-algebraic equations (DAEs) was presented. The designed procedure was based on variability constraints and reduced model of considered system equations, characterized by constant dynamics and linearized system of algebraic equations. A multiple shooting approach was applied to divide an independent variable range into assumed number of subintervals. This approach resulted in nonlinear optimization task (NLP) with pointwise-continuous constraints. Therefore, the presented procedure was based on the efficient nonlinear optimization algorithm. Finally, some implementation issues were discussed. The effectiveness of the presented methodology was presented on a process design task subject to a nonlinear differential-algebraic model of a chemical reactor.