Investigation of some starting protocols for BDF (FIRM) in electrochemical digital simulation

Starting procedures for the backward differentiation formula (BDF) method have been investigated for the simulation of a chronopotentiometric or chronoamperometric experiment. How to start a simulation becomes especially important if the second (spatial) derivative of concentration is approximated by a fourth-order difference formula. The method of Kimble and White (KW) has been adapted to provide high-accuracy starting values. A comparison with other starting procedures is made. Surprisingly, the simple BDF start with a time correction, as used by Feldberg and co-workers, although not as accurate as the KW start, is the most efficient method. Its efficiency (when using the higher-order spatial second derivative approximations) is shown to be almost the same as for the extrapolation technique which, as a one-step (in time) method, does not depend on a starting strategy.