DEVELOPMENT OF COMPUTATIONAL TECHNIQUES TO SOLVE PROBLEMS EXTERNAL AND INTERNAL BALLISTICS
- 1 Faculty of Cybernetics, Taras Shevchenko National University of Kyiv, Ukraine
The paper is dedicated to the improvement of existing and development of new mathematical methods for ballistics. We consider the interpolation of air drag function by using parabolic spline. Used spline does not require any additional conditions and is stablе. The efficiency of the application of parabolic spline for different drag functions is shown. The spline approximation demonstates good accuracy, saves the behavior of drag functions and can be used in models of external ballistics. The Dirichlet boundary value problem for the unsteady-state equation of convection-diffusion-reaction with the prevailing convection are presented too. For differencing is used the parabolic spline that is continuous together with its first-order derivative which does not demand any additional conditions for its construction. Search for solution of the task in the form of a spline is applied to time-discretizable equation of convection-diffusion-reaction. For the received of difference scheme its monotonicity is proved. Theoretical researches and results of numerous experiments show that the offered scheme for the equation of convection-diffusion-reaction allows to solve boundary value problem for the wide range of values of the equation coefficients. This applies especially cases when convection far exceeds diffusion. The monotonic scheme provides stability of the computational solution, and application of a parabolic spline for its construction allows to reproduce the solution in the form of continuous function for the timepoints determined by discretization. There are given examples of calculations for a case of domination of the convective term over diffusion one.