Adaptive stochastic methods : in computational mathematics and mechanics This monograph is devoted to developing adaptive stochastic methods of computational mathematics with the use of adaptively controlled computational procedures. We consider the base ideas of the algorithms ways to synthesise them and analyse their properties and efficiency while evaluating multidimensional integrals and solving integral equations of the theory of elasticity and the theory of heat conduction. The key feature of the approaches and results presented in this book consists of a comprehensive analysis of mechanisms of utilisation of adaptive control in statistical evaluation procedures which makes them converge much faster. This book is intended for all students of numerical methods mathematical statistics and methods of statistical simulation as well as for specialists in the fields of computational mathematics and mechanics Page v Introduction: statistical computing algorithms as a subject of adaptive control 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 Numerican 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