Adaptive Stochastic Methods: In Computational Mathematics and Mechanics (Hardcover)

Adaptive Stochastic Methods: In Computational Mathematics and Mechanics By Dmitry G. Arseniev, Vladimir M. Ivanov, Maxim L. Korenevsky Cover Image
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Description


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

About the Author


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


Product Details
ISBN: 9783110553642
ISBN-10: 3110553643
Publisher: de Gruyter
Publication Date: January 9th, 2018
Pages: 290
Language: English