New Results on the Quasilinearization Method for Time Scales

We have developed the generalized quasilinearization method (QM) for an initial value problem (IVP) of dynamic equations on time scales by using comparison theorems with a coupled lower solution (LS) and upper solution (US) of the natural type. Under some conditions, we observed that the solutions converged to the unique solution of the problem uniformly and monotonically, and the rate of convergence was investigated.