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The book contains an extensive illustration of use of finite difference method in solving the boundary value problem numerically. A wide class of differential equations has been numerically solved in this book. Starting with differential equations of elementary functions like hyperbolic, sine and cosine, we have solved those of special functions like Hermite, Laguerre and Legendre. Those of Airy function, of stationary localised wavepacket, of the quantum mechanical problem of a particle in a 1D box, and the polar equation of motion under gravitational interaction have also been solved. Mathematica 6.0 has been used to solve the system of linear equations that we encountered and to plot the numerical data. Comparison with known analytic solutions showed nearly perfect agreement in every case. On reading this book, readers will become adept in using the method.

Boundary value problems --- Finite differences. --- Applied physics. --- SCIENCE / Applied Sciences. --- Numerical solutions.

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Manifolds (Mathematics) --- Boundary value problems --- Elliptic operators --- Fokker-Planck equation --- Equation, Fokker-Planck --- Planck-Fokker equation --- Differential equations, Partial --- Stochastic differential equations --- Differential operators, Elliptic --- Operators, Elliptic --- Partial differential operators --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Geometry, Differential --- Topology --- Boundary value problems. --- Elliptic operators. --- Fokker-Planck equation. --- Variétés (mathématiques) --- Problèmes aux limites --- Opérateurs elliptiques --- Fokker-Planck, Équation de --- Problèmes aux limites. --- Opérateurs elliptiques. --- Fokker-Planck, Équation de.

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This book is concerned with several elliptic and parabolic obstacle-type problems with a focus on the cases where the free and fixed boundaries meet. The results presented complement those found in existing books in the subject, which mainly treat regularity properties away from the fixed boundary. The topics include optimal regularity, analysis of global solutions, tangential touch of the free and fixed boundaries, as well as Lipschitz- and $C^1$-regularity of the free boundary. Special attention is given to local versions of various monotonicity formulas. The intended audience includes research mathematicians and advanced graduate students interested in problems with free boundaries.

Global analysis (Mathematics). --- Mathematical optimization. --- Analysis. --- Calculus of Variations and Optimal Control; Optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Boundary value problems. --- Boundary conditions (Differential equations) --- Differential equations --- Mathematical physics --- Initial value problems --- Mathematical analysis. --- Analysis (Mathematics). --- Calculus of variations. --- Isoperimetrical problems --- Variations, Calculus of --- 517.1 Mathematical analysis

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The book investigates fundamental issues in flexible manipulator systems, including distributed parameter modeling and boundary controller design. It presents theoretical explorations of several fundamental problems concerning the dynamics and control of these systems. By integrating fresh concepts and results to form a systematic approach to control, it also provides a basic theoretical framework. In turn, the book offers a comprehensive treatment of flexible manipulator systems, addressing topics ranging from related distributed parameter modeling and advanced boundary controller design for these systems with input constraint, to active control with output constraint. In brief, the book addresses dynamical analysis and control design for flexible manipulator systems. Though primarily intended for researchers and engineers in the control system and mechanical engineering community, it can also serve as supplemental reading on the modeling and control of flexible manipulator systems at the postgraduate level.

Control theory --- Boundary value problems. --- Manipulators (Mechanism) --- Mathematics. --- Control. --- Engineering. --- Application software. --- Mechanical engineering. --- Robotics. --- Automation. --- Robotics and Automation. --- Computer Applications. --- Mechanical Engineering. --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Dynamics --- Machine theory --- Mechanical manipulators --- Robots, Industrial --- Robots --- Computer science. --- Engineering, Mechanical --- Engineering --- Machinery --- Steam engineering --- Informatics --- Science --- Application computer programs --- Application computer software --- Applications software --- Apps (Computer software) --- Computer software --- Automatic factories --- Automatic production --- Computer control --- Engineering cybernetics --- Factories --- Industrial engineering --- Mechanization --- Assembly-line methods --- Automatic control --- Automatic machinery --- CAD/CAM systems --- Robotics --- Automation

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This book presents methods for full-wave computer simulation that can be used in various applications and contexts, e.g. seismic prospecting, earthquake stability, global seismic patterns on Earth and Mars, medicine, traumatology, ultrasound investigation of the human body, ultrasound and laser operations, ultrasonic non-destructive railway testing, modelling aircraft composites, modelling composite material delamination, etc. The key innovation of this approach is the ability to study spatial dynamical wave processes, which is made possible by cutting-edge numerical finite-difference grid-characteristic methods. The book will benefit all students, researchers, practitioners and professors interested in numerical mathematics, computer science, computer simulation, high-performance computer systems, unstructured meshes, interpolation, seismic prospecting, geophysics, medicine, non-destructive testing and composite materials.

Numerical grid generation (Numerical analysis) --- Computational grids (Computer systems) --- Engineering. --- Artificial intelligence. --- Computer mathematics. --- Computational intelligence. --- Computational Intelligence. --- Artificial Intelligence (incl. Robotics). --- Operations Research/Decision Theory. --- Computational Science and Engineering. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Construction --- Industrial arts --- Technology --- Mathematics --- Grid computing --- Grids, Computational (Computer systems) --- Computer systems --- Cyberinfrastructure --- Coordinate generation, Numerical (Numerical analysis) --- Generation of numerical grids (Numerical analysis) --- Grid generation, Numerical (Numerical analysis) --- Mesh generation, Numerical (Numerical analysis) --- Numerical coordinate generation (Numerical analysis) --- Numerical mesh generation (Numerical analysis) --- Boundary value problems --- Differential equations, Partial --- Nets (Mathematics) --- Numerical analysis --- Numerical solutions --- Operations research. --- Computer science. --- Artificial Intelligence. --- Informatics --- Science --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Decision making. --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Decision making