Numerical Analysis of Systems of Ordinary and Stochastic Differential Equations (eBook)

I-VIII -- 1. Numerical Solution of the Cauchy Problem for Systems of Ordinary Differential Equations -- 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations -- 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.1. Elements of Probability Theory, Stochastic Processes and Statistical Simulation -- 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.2. Cauchy Problem for a SDE System. Main Definitions -- 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.3. Construction of SDEs with Given Probability Characteristics of Solution -- 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.4. Linear SDE Systems with Additive and Multiplicative Noise -- 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.5. Mean Square Stability of SDE Solutions. Stiff in Mean Square SDE Systems. Oscillatory Stochastic Systems -- 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.6. Simple Numerical Methods Generalizing the Explicit Runge-Kutta Methods -- 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.7. Families of Numerical Methods for Solving SDE Systems. Theorem of Convergence -- 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.8. Mean Square Consistency of Methods -- 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.9. Mean Square Stability of Methods -- 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.10. Numerical Methods for Solving Linear SDE Systems -- 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.11. Variable Step Algorithms for Solving SDEs -- 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.12. Numerical Solution of SDE System with Poisson Component -- 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.13. Applying SDE for Numerical Solution of Linear Elliptic and Parabolic Equations -- 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.14. Statistical Simulation of the SDE Solutions in Problems of Analysis and Synthesis of Automated Control -- 2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations. 2.15. Numerical Experiments -- References