Kontreras D. Methods and tools for computer realization of integro-differential models of dynamic systems

The thesis is devoted to a research of mathematical models of dynamic systems as the Volterra integro-differential equations and development of methods, algorithms and software for their computer realization. Is established, that an effective way to increase of efficiency of methods and tools for computer simulation of dynamic systems is the application of the Volterra integro-differential equations as mathematical models of these systems. The complex of quadrature-difference algorithms for simulation of a wide class of linear and nonlinear dynamic systems is designed. The method for the numerical solution of the integro-differential equations with a singular kernel, which grounded on the quadrature formulas of the opened type, is offered. The numerical algorithm for the solution of the boundary value problem for Volterra integro-differential equations is designed. The method of computer realization of nonlinear Volterra integro-differential models, grounded on automatic adaptations of quadrature methods of the decision of the integral equations is designed. The software package for the solution of a Cauchy problem and boundary value problem for Volterra integro-differential equation is designed. With the help of the designed algorithms and software the series of practical problems of simulation of the dynamic systems is solved.