Solving the space-time problem on the basis of quasi-stationary derivatives

The new method for solving the space-time problem is developed. The method is based upon the principle of quasi-stationary derivatives (QSD). The simplest case of this approach when the quasi-stationary first derivative used only is very close to the well-known “prompt jump” method. The using of second and other quasi-stationary derivatives leads to convergence of the QSD solution to exact space-time problem solution. The methodology of QSD approach is outlined, and accuracy and efficiency is demonstrated. The numerical results in ID geometry are presented.