Description

Book Synopsis

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

Adaptive Stochastic Methods: In Computational Mathematics and Mechanics

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    A Hardback by Dmitry G. Arseniev, Vladimir M. Ivanov, Maxim L. Korenevsky

    15 in stock

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      View other formats and editions of Adaptive Stochastic Methods: In Computational Mathematics and Mechanics by Dmitry G. Arseniev

      Publisher: De Gruyter
      Publication Date: Publication Date: 09/01/2018
      ISBN13: 9783110553642, 978-3110553642
      ISBN10:

      Description

      Book Synopsis

      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

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