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 : 86. 86 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.

Advanced Numerical Methods In Applied Sciences

Author : Luigi Brugnano
ISBN : 9783038976660
Genre : Juvenile Nonfiction
File Size : 38. 47 MB
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The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.

Finite Element Methods For Eigenvalue Problems

Author : Jiguang Sun
ISBN : 9781482254655
Genre : Mathematics
File Size : 38. 51 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 : 35. 54 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 : 39. 27 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.

Nonlinear Functional Analysis And Applications

Author : Advanced Seminar on Nonlinear Functional Analysis and Applications
ISBN : UCSC:32106006181934
Genre : Electronic books
File Size : 41. 46 MB
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This volume contains the proceedings of an advanced seminar conducted by the Mathematics Research Center at the University of Wisconsin, Madison, held on October 12-14, 1970. This collection of papers is intended to give a reasonably self-contained introduction to the basic concepts and techniques of this field, highlighted by a few significant applications.

Mathematical Reviews

Author :
ISBN : UVA:X006180725
Genre : Mathematics
File Size : 76. 60 MB
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Journal Of Physics A Mathematical And General

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ISBN : UCAL:B4491382
Genre :
File Size : 27. 21 MB
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Books In Series

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ISBN : STANFORD:36105015640415
Genre : Monographic series
File Size : 90. 26 MB
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Books In Series In The United States

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ISBN : UOM:39015058376966
Genre : Children's literature in series
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