edited by D G Arsenjev (St. Petersburg State Technical University, Russia) , V M Ivanov (St. Petersburg State Technical University, Russia) , & O Y Kul'chitsky (St. Petersburg State Technical University, Russia)

This book describes 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 in this book 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 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