Summary
International Symposium on Nonlinear Theory and its Applications
2009
Session Number:A4L-C
Session:
Number:A4L-C4
Implementation of implicit Runge-Kutta methods into circuit simulators for nonlinear circuits
Yasuhiko Tohyama, Jun Shirataki, Makiko Okumura,
pp.-
Publication Date:2009/10/18
Online ISSN:2188-5079
Summary:
This paper describes a method of implementing implicit Runge-Kutta(IRK) formulas into circuit simulators for nonlinear circuits as numerical integration. Equivalent circuits at discrete time of IRK formulas for linear and nonlinear elements are proposed. In IRK methods, the size of equivalent circuit becomes larger than the numerical integration in conventional circuit simulators, because the equivalent circuit at an intermediate time between past and present time are needed in addition to the equivalent circuit at present time. This problem is solved by using larger time step for numerical integration compared to conventional methods to save calculation time, since RadauIIA and LobattoIIIA of IRK formulas have high orders and are A-stable. The IRK and conventional methods are compared in terms of accuracy and computational costs by using an example circuit.