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 : 74. 28 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.

Finite Element Methods For Eigenvalue Problems

Author : Jiguang Sun
ISBN : 9781482254655
Genre : Mathematics
File Size : 47. 6 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.

Stochastic Cauchy Problems In Infinite Dimensions

Author : Irina V. Melnikova
ISBN : 9781482210514
Genre : Mathematics
File Size : 21. 74 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.

Reconstruction From Integral Data

Author : Victor Palamodov
ISBN : 9781498710114
Genre : Mathematics
File Size : 54. 92 MB
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Reconstruction of a function from data of integrals is used for problems arising in diagnostics, including x-ray, positron radiography, ultrasound, scattering, sonar, seismic, impedance, wave tomography, crystallography, photo-thermo-acoustics, photoelastics, and strain tomography. Reconstruction from Integral Data presents both long-standing and recent mathematical results from this field in a uniform way. The book focuses on exact analytic formulas for reconstructing a function or a vector field from data of integrals over lines, rays, circles, arcs, parabolas, hyperbolas, planes, hyperplanes, spheres, and paraboloids. It also addresses range characterizations. Coverage is motivated by both applications and pure mathematics. The book first presents known facts on the classical and attenuated Radon transform. It then deals with reconstructions from data of ray (circle) integrals. The author goes on to cover reconstructions in classical and new geometries. The final chapter collects necessary definitions and elementary facts from geometry and analysis that are not always included in textbooks.

Mathematical Modelling Of Waves In Multi Scale Structured Media

Author : Alexander B. Movchan
ISBN : 9781498782104
Genre : Mathematics
File Size : 78. 93 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.

Angewandte Funktionalanalysis

Author : Manfred Dobrowolski
ISBN : 9783642152696
Genre : Mathematics
File Size : 86. 45 MB
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In dem Lehrbuch werden die Methoden der Funktionalanalysis mit ihren Anwendungen in der Theorie elliptischer Differentialgleichungen behandelt. Gleichzeitig werden Lesern die analytischen und funktionalanalytischen Sätze näher gebracht, die für die numerische Approximation von Differentialgleichungen bedeutsam sind. Neben dem klassischen Stoff werden daher die Sobolevschen Funktionenräume sowie die Existenz- und Regularitätstheorie elliptischer Differentialgleichungen ausführlich dargestellt. Mit vielen Anwendungsbeispielen und Übungsaufgaben.

Pascal Fermat Und Die Berechnung Des Gl Cks

Author : Keith J. Devlin
ISBN : 3406590993
Genre : Wahrscheinlichkeitstheorie - Geschichte
File Size : 39. 47 MB
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Der Autor stellt die Entstehung der Wahrscheinlichkeitsrechnung und den damit verbundenen Wandel des menschlichen Alltagslebens dar.

Psychologie Der Intelligenz

Author : Jean Piaget
ISBN : 3608940146
Genre :
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Journal Of Physics A Mathematical And General

Author :
ISBN : UCAL:B4491382
Genre :
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Die China Study Und Ihre Verbl Ffenden Konsequenzen F R Die Lebensf Hrung

Author : Thomas Colin Campbell
ISBN : 3927344915
Genre :
File Size : 90. 93 MB
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