Arseniev / Ivanov / Korenevsky Adaptive Stochastic Methods

In Computational Mathematics and Mechanics
1. Auflage 2018
ISBN: 978-3-11-055367-3
Verlag: De Gruyter
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 290 Seiten

This monograph develops adaptive stochastic methods in computational mathematics. The authors discuss the basic ideas of the algorithms and ways to analyze their properties and efficiency. Methods of evaluation of multidimensional integrals and solutions of integral equations are illustrated by multiple examples from mechanics, theory of elasticity, heat conduction and fluid dynamics.

Contents

Part I: Evaluation of Integrals
Fundamentals of the Monte Carlo Method to Evaluate Definite Integrals
Sequential Monte Carlo Method and Adaptive Integration
Methods of Adaptive Integration Based on Piecewise Approximation
Methods of Adaptive Integration Based on Global Approximation
Numerical Experiments
Adaptive Importance Sampling Method Based on Piecewise Constant Approximation

Part II: Solution of Integral Equations
Semi-Statistical Method of Solving Integral Equations Numerically
Problem of Vibration Conductivity
Problem on Ideal-Fluid Flow Around an Airfoil
First Basic Problem of Elasticity Theory
Second Basic Problem of Elasticity Theory
Projectional and Statistical Method of Solving Integral Equations Numerically

Zielgruppe

Researchers in Mathematics and Physics as well as in Mechanical E

Autoren/Hrsg.

Arseniev, Dmitry G.

Ivanov, Vladimir M.

Korenevsky, Maxim L.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Regelungstechnik
• Mathematik | Informatik Mathematik Stochastik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau

Über Autor(innen)

Dmitry Arsenyev, Vladimir Ivanov and Maxim Korenevskii, St. Petersburg Polytechnical University, Russia.