Numerical Stability of Lumped Constant Model for VBL Dynamics

An implicit method is used to improve the stability of the numerical simulation of vertical Bloch line motion. In the equations of motion, VR, VS and ¿a are replaced by their respective changes per time increment ¿T. The values of the various force terms at a future time T + ¿T are estimated from their values at time T using appropriate correction terms, and a system of simultaneous linear equations in ¿R, ¿¿a and ¿S is obtained for each domain wall point. Whereas explicit solutions are numerically stable for ¿T as large as 0.2 ns, this implicit solution is stable for ¿T taken as large as 16 ns.