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

Abstract

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 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.