line integral methods for conservative problems monographs and research notes in mathematics

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Line Integral Methods For Conservative Problems

Author : Luigi Brugnano
ISBN : 9781482263855
Genre : Mathematics
File Size : 43. 92 MB
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Line Integral Methods for Conservative Problems explains the numerical solution of differential equations within the framework of geometric integration, a branch of numerical analysis that devises numerical methods able to reproduce (in the discrete solution) relevant geometric properties of the continuous vector field. The book focuses on a large set of differential systems named conservative problems, particularly Hamiltonian systems. Assuming only basic knowledge of numerical quadrature and Runge–Kutta methods, this self-contained book begins with an introduction to the line integral methods. It describes numerous Hamiltonian problems encountered in a variety of applications and presents theoretical results concerning the main instance of line integral methods: the energy-conserving Runge–Kutta methods, also known as Hamiltonian boundary value methods (HBVMs). The authors go on to address the implementation of HBVMs in order to recover in the numerical solution what was expected from the theory. The book also covers the application of HBVMs to handle the numerical solution of Hamiltonian partial differential equations (PDEs) and explores extensions of the energy-conserving methods. With many examples of applications, this book provides an accessible guide to the subject yet gives you enough details to allow concrete use of the methods. MATLAB codes for implementing the methods are available online.

Iterative Methods And Preconditioning For Large And Sparse Linear Systems With Applications

Author : Daniele Bertaccini
ISBN : 9781498764179
Genre : Mathematics
File Size : 31. 32 MB
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This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.

Finite Element Methods For Eigenvalue Problems

Author : Jiguang Sun
ISBN : 9781482254655
Genre : Mathematics
File Size : 32. 45 MB
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This book covers finite element methods for several typical eigenvalues that arise from science and engineering. Both theory and implementation are covered in depth at the graduate level. The background for typical eigenvalue problems is included along with functional analysis tools, finite element discretization methods, convergence analysis, techniques for matrix evaluation problems, and computer implementation. The book also presents new methods, such as the discontinuous Galerkin method, and new problems, such as the transmission eigenvalue problem.

Mathematical Modelling Of Waves In Multi Scale Structured Media

Author : Alexander B. Movchan
ISBN : 9781498782104
Genre : Mathematics
File Size : 54. 13 MB
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Mathematical Modelling of Waves in Multi-Scale Structured Media presents novel analytical and numerical models of waves in structured elastic media, with emphasis on the asymptotic analysis of phenomena such as dynamic anisotropy, localisation, filtering and polarisation as well as on the modelling of photonic, phononic, and platonic crystals.

Stochastic Cauchy Problems In Infinite Dimensions

Author : Irina V. Melnikova
ISBN : 9781482210514
Genre : Mathematics
File Size : 23. 73 MB
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Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory. The book presents generalized solutions to the Cauchy problem in its initial form with white noise processes in spaces of distributions. It also covers the "classical" approach to stochastic problems involving the solution of corresponding integral equations. The first part of the text gives a self-contained introduction to modern semi-group and abstract distribution methods for solving the homogeneous (deterministic) Cauchy problem. In the second part, the author solves stochastic problems using semi-group and distribution methods as well as the methods of infinite-dimensional stochastic analysis.

Trend And Applications Of Mathematics To Mechanics

Author : S. Rionero
ISBN : 9788847003545
Genre : Technology & Engineering
File Size : 29. 53 MB
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Essential Mathematics For Political And Social Research

Author : Jeff Gill
ISBN : 9780521834261
Genre : Mathematics
File Size : 61. 67 MB
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This 2006 book addresses the comprehensive introduction to the mathematical principles needed by modern social scientists.

Psychology Of Intelligence Analysis

Author : Richards J. Heuer
ISBN : 9780160590351
Genre : Psychology
File Size : 23. 13 MB
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Finite Volume Methods For Hyperbolic Problems

Author : Randall J. LeVeque
ISBN : 9781139434188
Genre : Mathematics
File Size : 32. 53 MB
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This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.

Qualitative And Asymptotic Analysis Of Differential Equations With Random Perturbations

Author : Anatoliy M. Samoilenko
ISBN : 9789814329071
Genre : Differential equations
File Size : 31. 33 MB
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Differential equations with random perturbations are the mathematical models of real-world processes that cannot be described via deterministic laws, and their evolution depends on random factors. The modern theory of differential equations with random perturbations is on the edge of two mathematical disciplines: random processes and ordinary differential equations. Consequently, the sources of these methods come both from the theory of random processes and from the classic theory of differential equations. This work focuses on the approach to stochastic equations from the perspective of ordinary differential equations. For this purpose, both asymptotic and qualitative methods which appeared in the classical theory of differential equations and nonlinear mechanics are developed.

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