Adaptive stochastic methods : in computational mathematics and mechanics / Dmitry G. Arseniev, Vladimir M. Ivanov, Maxim L. Korenevsky.

Format:

Book

Author/Creator:

Arsenʹev, D. G. (Dmitriĭ Germanovich), 1963- author.

Contributor:

Ivanov, V. M. (Vladimir Mikhaĭlovich), 1956- editor.

Korenevskiĭ, M. L. (Maksim Lʹvovich), editor.

Language:

English

Subjects (All):

Stochastic processes.

Stochastic integrals.

Adaptive control systems.

Physical Description:

1 online resource (xi, 278 pages)

Edition:

1st ed.

Place of Publication:

Berlin ; Boston : De Gruyter, 2018.

Language Note:

In English.

Summary:

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 IntegralsFundamentals of the Monte Carlo Method to Evaluate Definite IntegralsSequential Monte Carlo Method and Adaptive IntegrationMethods of Adaptive Integration Based on Piecewise ApproximationMethods of Adaptive Integration Based on Global ApproximationNumerical ExperimentsAdaptive Importance Sampling Method Based on Piecewise Constant Approximation Part II: Solution of Integral EquationsSemi-Statistical Method of Solving Integral Equations NumericallyProblem of Vibration ConductivityProblem on Ideal-Fluid Flow Around an AirfoilFirst Basic Problem of Elasticity TheorySecond Basic Problem of Elasticity TheoryProjectional and Statistical Method of Solving Integral Equations Numerically

Contents:

Frontmatter

Preface

Contents

Introduction: Statistical Computing Algorithms as a Subject of Adaptive Control

Part I: Evaluation of Integrals

1. Fundamentals of the Monte Carlo Method to Evaluate Definite Integrals

2. Sequential Monte Carlo Method and Adaptive Integration

3. Methods of Adaptive Integration Based on Piecewise Approximation

4. Methods of Adaptive Integration Based on Global Approximation

5. Numerical Experiments

6. Adaptive Importance Sampling Method Based on Piecewise Constant Approximation

Part II: Solution of Integral Equations

7. Semi-Statistical Method of Solving Integral Equations Numerically

8. Problem of Vibration Conductivity

9. Problem on Ideal-Fluid Flow Around an Airfoil

10. First Basic Problem of Elasticity Theory

11. Second Basic Problem of Elasticity Theory

12. Projectional and Statistical Method of Solving Integral Equations Numerically

Afterword

Bibliography

Index

Notes:

Description based on print version record.

ISBN:

9783110553673

3110553678

OCLC:

1024020911