Введение
Chapter 1. Implicit one-step methods (with fixed step size) for functional differential equations 12
1. Statement of the problem 12
2. Implicit Euler method with piece-wise constant interpolation 13
3. Interpolation and extrapolation of the model pre-history . 16
3.1. Interpolating operators 16
3.2. Extrapolating operators 19
3.3. Interpolating-extrapolating operator 21
4. Implicit Runge-Kutta-like methods 21
4.1. General scheme 22
4.2. Convergence order 25
4.3. Approximation order 27
4.4. Potential for parallel computation 31
4.5. On the structure of functionals 32
Chapter 2. Numerical algorithms (with variable step size) for functional differential equations 34
5. Description of IRK-methods with variable step size control . 34
6. Convergence order 37
7. Methods of interpolation and extrapolation of the extended pre-history of discrete model 39
8. Choice of the step size 43
9. Numerical modeling of control time-delay system 45
Chapter 3. Testing and comparing explicit and implicit Runge—Kutta—like methods for functional differential equa tions 49
10. Realization and comparing explicit and implicit numerical methods with fixed step size 50
10.1. Testing of explicit and implicit Euler methods . 50
10.2. High order methods with fixed step size 63
11. Explicit and implicit methods with automatic step size control 66
11.1. Explicit Runge-Kutta-like method of 2(3) order with automatic step size control 66
11.2. Implicit trapezoidal method with interpolation and automatic step size control 67
12. Model examples (medicine and control theory) 79
12.1. HIV-infection model 79
12.2. Modeling of the linear quadratic control problem with delay 81
Bibliography 86
