Numerical Analysis of Systems of Ordinary and Stochastic Differential Equations / / S. S. Artemiev, T. A. Averina.

• Superior document: Title is part of eBook package: De Gruyter DGBA Mathematics - 1990 - 1999
• VerfasserIn: Artemiev, S. S.,; Averina, T. A.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2011]; ©1997
• Year of Publication: 2011
• Edition: Reprint 2010
• Language: English
• Physical Description: 1 online resource (176 p.)

Table of Contents

• 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