Elementary differentials,their graphs and codes

When designing high-order one-step numerical methods like Runge-Kutta, Rosenbrock, or ABC-schemes for solving ordinary differential equations, one has to take into account many tens and hundreds of elementary differentials. Graphical representation of the latter in use nowadays does not solve the problem of the computerization of the enormous amount of manual work. We have proposed a simple and intuitive way of digital coding of elementary differentials or their graphs. Algorithms for generation, analysis, and synthesis of such codes were developed and implemented in a computer program, which computes tables of codes for elementary differentials of any order together with their multiplicities and gamma-factors.