Umfang:
Online-Ressource (vi, 176 p)
Ausgabe:
Reproduktion 2011
ISBN:
9783110944662
,
9067642509
,
9789067642507
Inhalt:
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)
Anmerkung:
Includes bibliographical references
,
Im Original erschienen 1997
,
Systemvoraussetzung: Internet-Anschluss; Adobe Acrobat Reader
,
Preface; 1. Numerical Solution of the Cauchy Problem for Systems of Ordinary Differential Equations; 1.1. The Cauchy Problem for an ODE System. Linear Systems. Stiff Systems; 1.2. Single-step Methods. Main Definitions; 1.3. Rosenbrock Type Methods. The Convergence Theorem; 1.4. Taylor Expansion of Exact and Numerical Solutions of the Cauchy Problem; 1.5. Consistency of RTMs; 1.6. A-stability of RTMs; 1.7. Practical Applications of RTMs to the Solution of Stiff ODEs; 1.8. Some Generalizations of RTMs; 1.9. Numerical Experiments
,
2. Statistical Simulation of the Cauchy Problem Solution for Systems of Stochastic Differential Equations2.1. Elements of Probability Theory, Stochastic Processes and Statistical Simulation; 2.2. Cauchy Problem for a SDE System. Main Definitions; 2.3. Construction of SDEs with Given Probability Characteristics of Solution; 2.4. Linear SDE Systems with Additive and Multiplicative Noise; 2.5. Mean Square Stability of SDE Solutions. Stiff in Mean Square SDE Systems. Oscillatory Stochastic Systems; 2.6. Simple Numerical Methods Generalizing the Explicit Runge-Kutta Methods
,
2.7. Families of Numerical Methods for Solving SDE Systems. Theorem of Convergence2.8. Mean Square Consistency of Methods; 2.9. Mean Square Stability of Methods; 2.10. Numerical Methods for Solving Linear SDE Systems; 2.11. Variable Step Algorithms for Solving SDEs; 2.12. Numerical Solution of SDE System with Poisson Component; 2.13. Applying SDE for Numerical Solution of Linear Elliptic and Parabolic Equations; 2.14. Statistical Simulation of the SDE Solutions in Problems of Analysis and Synthesis of Automated Control; 2.15. Numerical Experiments; References
,
In English
Weitere Ausg.:
ISBN 9067642509
Weitere Ausg.:
ISBN 9789067642507
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Artemjev, S. S. Numerical analysis of systems of ordinary and stochastic differential equations Utrecht : VSP, 1997 ISBN 9067642509
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Gewöhnliche Differentialgleichung
;
Stochastische Differentialgleichung
;
Numerische Mathematik
DOI:
10.1515/9783110944662
URL:
Volltext
(lizenzpflichtig)
