Scale and modify for the second and third order BDF methods

This paper investigates a ‘scale and modify’ technique used with variable stepsize BDF methods. When the stepsize is changed using the usual scaling procedure for Nordsieck methods, there can be adverse affects on the stability unless a severe restriction is placed on the allowable stepsize ratios. However, a modification to this scaling procedure may extend the range of permissible stepsize ratios. Results for the Nordsieck form of the second and third order methods indicate that this may be possible.