Random Ordinary Differential Equations and Their Numerical Solution

Part I. Random and Stochastic Ordinary Differential Equations

1. Introduction
Xiaoying Han, Peter E. Kloeden

2. Random Ordinary Differential Equations
Xiaoying Han, Peter E. Kloeden

3. Stochastic Differential Equations
Xiaoying Han, Peter E. Kloeden

4. Random Dynamical Systems
Xiaoying Han, Peter E. Kloeden

5. Numerical Dynamics
Xiaoying Han, Peter E. Kloeden

Part II. Taylor Expansions

6. Taylor Expansions for Ordinary and Stochastic Differential Equations
Xiaoying Han, Peter E. Kloeden

7. Taylor Expansions for RODEs with Affine Noise
Xiaoying Han, Peter E. Kloeden

8. Taylor-Like Expansions for General Random Ordinary Differential Equations
Xiaoying Han, Peter E. Kloeden

Part III. Numerical Schemes for Random Ordinary Differential Equations

9. Numerical Methods for Ordinary and Stochastic Differential Equations
Xiaoying Han, Peter E. Kloeden

10. Itô–Taylor Schemes for RODEs with Itô Noise
Xiaoying Han, Peter E. Kloeden

11. Numerical Schemes for RODEs with Affine Noise
Xiaoying Han, Peter E. Kloeden

12. RODE-Taylor Schemes: General Case
Xiaoying Han, Peter E. Kloeden

13. Numerical Stability
Xiaoying Han, Peter E. Kloeden

14. Stochastic Integrals: Simulation and Approximation
Xiaoying Han, Peter E. Kloeden

Part IV. Random Ordinary Differential Equations in the Life Sciences

15. Comparative Simulations of Biological Systems
Xiaoying Han, Peter E. Kloeden

16. Chemostat
Xiaoying Han, Peter E. Kloeden

17. Immune System Virus Model
Xiaoying Han, Peter E. Kloeden

18. Random Markov Chains
Xiaoying Han, Peter E. Kloeden

Keywords: Mathematics, Probability Theory and Stochastic Processes, Numeric Computing, Ordinary Differential Equations, Mathematical and Computational Biology