Adaptive Methods of Computing Mathematics and Mechanics
Stochastic Variant

A description of the adaptive methods of statistical numerical analysis using evaluation of integrals, solution of integral equations, boundary value problems of the theory of elasticity and heat conduction as examples. It explores the mechanisms of adaptation of statistical evaluation procedures.

A description of the adaptive methods of statistical numerical analysis using evaluation of integrals, solution of integral equations, boundary value problems of the theory of elasticity and heat conduction as examples. The results and approaches provided are different from those available in the literature, as detailed descriptions of the mechanisms of adaptation of statistical evaluation procedures, which accelerate their convergence, are given.

Evaluation of integrals and solution of integral equations - fundamentals of the Monte-Carlo method
evaluation of integrals by means of statistic simulation
employing adaptation
semi-statistical method of numerical solving integral equations
projection-statistical method of numerical solution of integral equations
the problem of vibration conductivity
the first basic problem of the elasticity theory
the second basic problem of the elasticity theory
a way to solve non-stationary problems
the random walk method
solution of boundary-value problems - introduction to the random walk method (RWM)
numerical solution of the heat conductivity problems by means of the random walk method
the Monte-Carlo method applied to problems of plate curving
the Monte-Carlo method applied to the flat problems of elasticity theory
application of Monte-Carlo method towards finding of tensions at dangerous points of cog-wheels
the spatial problem of heat conductivity
optimization of an FEM Grid - optimal distribution of nodes for the problem of tension of a balk of variable section
optimization in the general case
numerical simulation
BEMM optimal nodes with variable section, linear with respect to the length connection between optimal determinate nodes and optimal density
results of numerical experiments.