Interpolation Quadrature And Stochastic Integration

Interpolation, Quadrature and Stochastic Integration

Adaptive Stochastic Methods

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

Stochastic Dynamic Response and Stability of Ships and Offshore Platforms

This textbook investigates in detail the methods for stochastic dynamic response and stability analyses of nonlinear systems (especially ships and ocean engineering systems), elucidating the advantages and disadvantages of each of the methods (the statistical linearization method, the perturbation method, the Monte Carlo Simulation method, the numerical path integration method, the global geometric method and the first passage theory). Studies on stochastic dynamic analysis of nonlinear systems have attracted engineers and scientists from various disciplines, such as aeronautical, civil, mechanical and ocean engineering. Pursuing a systematic approach, this book establishes a fundamental framework for this topic, while emphasizing the importance of accurate and efficient analysis as well as the significant influence of choosing a suitable method in the design and optimization of various nonlinear engineering systems (especially ships and ocean engineering systems). The textbook is intended for upper undergraduate and graduate students who are interested in advanced dynamic analysis technologies, researchers investigating nonlinear systems under stochastic dynamic excitations, and civil/mechanical/structural/ocean engineers working on designing and optimization of real-world nonlinear engineering systems. The basis of English translation of this book from its Chinese original manuscript was done with the help of artificial intelligence. A subsequent human revision of the content was done by the author.