A Family of ESDIRK Integration Methods
This work provides new ESDIRK methods with embedded error estimation and continuous extensions for hybrid systems, which is an incremental contribution to numerical integration methods.
The paper derives and analyzes a family of explicit singly diagonal implicit Runge-Kutta (ESDIRK) integration methods with error estimators and continuous extensions for orders 1(2), 2(3), and 3(4), enabling low to medium accuracy solutions for ODEs and index-1 DAEs, and extending existing ESDIRK methods for hybrid systems with discrete events.
In this paper we derive and analyze the properties of explicit singly diagonal implicit Runge-Kutta (ESDIRK) integration methods. We discuss the principles for construction of Runge-Kutta methods with embedded methods of different order for error estimation and continuous extensions for discrete event location. These principles are used to derive a family of ESDIRK integration methods with error estimators and continuous-extensions. The orders of the advancing method (and error estimator) are 1(2), 2(3) and 3(4), respectively. These methods are suitable for obtaining low to medium accuracy solutions of systems of ordinary differential equations as well as index-1 differential algebraic equations. The continuous extensions facilitates solution of hybrid systems with discrete-events. Other ESDIRK methods due to Kværnø are equipped with continuous-extensions as well to make them applicable to hybrid systems with discrete events.