Chapman and Hall/CRC
408 pages | 57 B/W Illus.
Modelling with Ordinary Differential Equations: A Comprehensive Approach aims to provide a broad and self-contained introduction to the mathematical tools necessary to investigate and apply ODE models. The book starts by establishing the existence of solutions in various settings and analysing their stability properties. The next step is to illustrate modelling issues arising in the calculus of variation and optimal control theory that are of interest in many applications. This discussion is continued with an introduction to inverse problems governed by ODE models and to differential games.
The book is completed with an illustration of stochastic differential equations and the development of neural networks to solve ODE systems. Many numerical methods are presented to solve the classes of problems discussed in this book.
1. Introduction. 2. Elementary solution methods for simple ODEs. 3. Theory of ordinary differential calculation. 4. Systems of oridinary differentail equations. 5. Ordinary differential equations of order n. 6.Stability of ODE systems. 7. Boundary and eigenvalue problems. 8. Numerical solution of ODE problems. 9. ODEs and the calculus of variations. 10. Optimal control of ODE models. 11. Inverse problems with ODE models. 12. Differential games. 13. Stochastic differential equations. 14. Neural networks and ODE problems.