This paper deals with the solvability of initial-value problems (IVPs) and multipoint boundaryvalue problems (MPBVPs) for linear implicit non-autonomous systems of difference equations.

In this paper, we study the convergence of solutions to dynamic equations x = f (t, x) on time scales {T n } ∞ n=1 when this sequence converges to the time scale T. The convergent rate of solutions is estimated when f satisfies the Lipschitz condition in both variables. By a general view, we derive a new approach to the approximation of dynamic equations on time scales, especially the Euler method for differential equations. Some examples are given to illustrate our results.

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This paper deals with some classes of nonlinear implicit difference equations obtained via discretization of nonlinear differential-algebraic or partial differential-algebraic equations. The unique solvability of discretized problems is proved and the compatibility between index notions for nonlinear differential-algebraic equations and nonlinear implicit difference equations is studied.