Numerical analysis of systems of ordinary and stochastic differential equations / S.S. Artemiev and T.A. Averina.

Format:

Book

Author/Creator:

Artemiev, S. S.

Contributor:

Averina, T. A.

Language:

English

Subjects (All):

Differential equations--Numerical solutions.

Differential equations.

Physical Description:

1 online resource (184 p.)

Edition:

Reprint 2010

Place of Publication:

Utrecht, the Netherlands : VSP, 1997.

Language Note:

English

Summary:

This text deals with numerical analysis of systems of both ordinary and stochastic differential equations. It covers numerical solution problems of the Cauchy problem for stiff ordinary differential equations (ODE) systems by Rosenbrock-type methods (RTMs).

Contents:

Frontmatter

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

Notes:

Description based upon print version of record.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

Includes bibliographical references.

ISBN:

9783110944662

3110944669

OCLC:

843635120