دانلود کتاب Numerical Analysis of Systems of Ordinary and Stochastic Differential Equations

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Preface\n1. Numerical Solution of the Cauchy Problem for Systems of Ordinary Differential Equations\n1.1. The Cauchy Problem for an ODE System. Linear Systems. Stiff Systems\n1.2. Single-step Methods. Main Definitions\n1.3. Rosenbrock Type Methods. The Convergence Theorem\n1.4. Taylor Expansion of Exact and Numerical Solutions of the Cauchy Problem\n1.5. Consistency of RTMs\n1.6. A-stability of RTMs\n1.7. Practical Applications of RTMs to the Solution of Stiff ODEs\n1.8. Some Generalizations of RTMs\n1.9. Numerical Experiments\n2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations\n2.1. Elements of Probability Theory, Stochastic Processes and Statistical Simulation\n2.2. Cauchy Problem for a SDE System. Main Definitions\n2.3. Construction of SDEs with Given Probability Characteristics of Solution\n2.4. Linear SDE Systems with Additive and Multiplicative Noise\n2.5. Mean Square Stability of SDE Solutions. Stiff in Mean Square SDE Systems. Oscillatory Stochastic Systems\n2.6. Simple Numerical Methods Generalizing the Explicit Runge-Kutta Methods\n2.7. Families of Numerical Methods for Solving SDE Systems. Theorem of Convergence\n2.8. Mean Square Consistency of Methods\n2.9. Mean Square Stability of Methods\n2.10. Numerical Methods for Solving Linear SDE Systems\n2.11. Variable Step Algorithms for Solving SDEs\n2.12. Numerical Solution of SDE System with Poisson Component\n2.13. Applying SDE for Numerical Solution of Linear Elliptic and Parabolic Equations\n2.14. Statistical Simulation of the SDE Solutions in Problems of Analysis and Synthesis of Automated Control\n2.15. Numerical Experiments\nReferences