Model development and optimization
The author introduces the concept of evolutionary systems, brings various examples of such systems and introduces their mathematical models. The monograph contains both theoretical and applied aspects. It is divided into 3 parts and 14 chapters. The first part deals with the general theory. The mathematical models of the evolutionary systems are introduced in principle as nonlinear systems of integral-functional equations under some restrictions. The investigation of special models makes possible to find some now qualitative and quantitative results about new properties of the evolutionary systems. This theoretical part concentrates mainly on the existence and uniqueness of solutions for the systems of equations representing the mathematical models and considers optimization problems arising in connection with the investigation of properties of such models. The second part focuses on optimal numerical methods. The author investigates the solution of Volterra integral equations with pre-assigned accuracy by the optimal numerical methods and shows that many problems can be reduced to the solution of Volterra-type equations. The third part of the book is devoted to applications to economics, biology, immunology and health care. A special section is devoted to the history of the issue showing that the monograph is a further development of the ideas by L. V. Kantorovich, V. M. Glushkov and that its material was influenced by some ideas of V. I. Vernadsky and G. I. Marchuk.
nonlinear systems of integral-functional equations
scientific article; zbMATH DE number 1349362