The Taylor series method of order p and Adams–Bashforth method on time scales

A recent study on the Taylor series method of second order and the trapezoidal rule for dynamic equations on time scales has been continued by introducing a derivation of the Taylor series method of arbitrary order $p$ on time scales. The error and convergence analysis of the method is also obtained. The 2-step Adams–Bashforth method for dynamic equations on time scales is concluded and applied to examples of initial value problems for nonlinear dynamic equations. Numerical results are presented and discussed.