The Method of Referred Derivatives: a new technique for solving implicit equations in dynamic simulation

Abstract

Stiffness in simulation may be reduced or avoided by using algebraic equations to replace the differential equations describing the parts of the model with very, fast dynamics. However, if the resulting simultaneous equations are nonlinear, an implicit set of equations may arise for which no direct method of solution is possible. This paper sets out a novel method for converting such equations into an equivalent set of linear equations which may be solved for the time-derivatives of the original variables, either explicitly or by Gauss elimination. These derivatives may then be integrated along with the derivatives found in the normal way for the slower system states. A worked example of a flow network is provided to illustrate the robustness and practical significance of the method.