Abstract
The second-order backward-difference (BDF2) method requires solutions at two previous time steps and is often started with the first-order backward-difference (BDF1) method. The initial time step is typically taken to be small in order to minimize the effect of the first-order error. However, contrary to expectations, the solution computed in this way generates a very large error for stiff problems and the error grows as the initial time step is further reduced. As shown in this note, the problem is originated from the fact that the variable-coefficient BDF2 method combined with any first- or higher-order one-step method is asymptotically equivalent to the trapezoidal method and therefore not L-stable. Based on the study presented, it is strongly recommended that BDF2 method be started with a self-starting second-order implicit Runge-Kutta method, which guarantees second-order accuracy and L-stability at no additional cost.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
