EAN: 9783110553642

ADAPTIVE STOCHASTIC METHODS - DMITRY G ARSENIEV...

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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