ON THE CONVERGENCE OF SOLUTIONS TO NABLA DYNAMIC EQUATIONS ON TIME SCALES

This paper deals with the convergence of solutions to nabla dynamic equations x ^∇ = f (t, x) on time scales {Tn}^∞_n=1 when this sequence converges to the time scale T. The convergent rate of solutions is evaluated when f satisfies the Lipschitz condition in both variables. A new approach to the approximation of dynamic equations on time scales is derived by a general view, especially the implicit Euler method for differential equations. Some examples are given to illustrate results.