Analysis and implementation of TR-BDF2
This paper deals with the successful and popular one-step method, TR-BDF2, for the solution of systems of ordinary differential equations arising in circuit and device simulation [see \textit{R. E. Bank}, \textit{W. M. Coughran jun.}, \textit{W. Fichtner}, \textit{E. H. Grosse}, \textit{D. J. Rose} and \textit{R. K. Smith}, Transient simulation of silicon devices and circuits, IEEE Trans. Comput.-Aided Design 4, 436-451 (1985)]. This method can be viewed as an embedded diagonally implicit Runge-Kutta pair of orders 2 and 3. A detailed inspection yields new results on stability, continuous extension, implementation and on improved local error estimates. Numerical examples show the effectiveness of the refined method.
embedded diagonally implicit Runge-Kutta pair
scientific article; zbMATH DE number 897528
scientific article