Green's Functions and Finite Elements
Green's Functions and Finite Elements

Author: Friedel Hartmann

Publisher: Springer Science & Business Media

Published: 2012-08-01

Total Pages: 335

ISBN-13: 3642295231

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This book elucidates how Finite Element methods look like from the perspective of Green’s functions, and shows new insights into the mathematical theory of Finite Elements. Practically, this new view on Finite Elements enables the reader to better assess solutions of standard programs and to find better model of a given problem. The book systematically introduces the basic concepts how Finite Elements fulfill the strategy of Green’s functions and how approximating of Green’s functions. It discusses in detail the discretization error and shows that are coherent with the strategy of “goal oriented refinement”. The book also gives much attention to the dependencies of FE solutions from the parameter set of the model.

Green’s Functions in the Theory of Ordinary Differential Equations
Green’s Functions in the Theory of Ordinary Differential Equations

Author: Alberto Cabada

Publisher: Springer Science & Business Media

Published: 2013-11-29

Total Pages: 180

ISBN-13: 1461495067

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This book provides a complete and exhaustive study of the Green’s functions. Professor Cabada first proves the basic properties of Green's functions and discusses the study of nonlinear boundary value problems. Classic methods of lower and upper solutions are explored, with a particular focus on monotone iterative techniques that flow from them. In addition, Cabada proves the existence of positive solutions by constructing operators defined in cones. The book will be of interest to graduate students and researchers interested in the theoretical underpinnings of boundary value problem solutions.

Green, Brown, And Probability And Brownian Motion On The Line
Green, Brown, And Probability And Brownian Motion On The Line

Author: Kai Lai Chung

Publisher: World Scientific Publishing Company

Published: 2002-05-06

Total Pages: 188

ISBN-13: 9813102527

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This invaluable book consists of two parts. Part I is the second edition of the author's widely acclaimed publication Green, Brown, and Probability, which first appeared in 1995. In this exposition the author reveals, from a historical perspective, the beautiful relations between the Brownian motion process in probability theory and two important aspects of the theory of partial differential equations initiated from the problems in electricity — Green's formula for solving the boundary value problem of Laplace equations and the Newton-Coulomb potential.Part II of the book comprises lecture notes based on a short course on “Brownian Motion on the Line” which the author has given to graduate students at Stanford University. It emphasizes the methodology of Brownian motion in the relatively simple case of one-dimensional space. Numerous exercises are included.

Probabilistic Methods in Applied Mathematics
Probabilistic Methods in Applied Mathematics

Author: A. T. Bharucha-Reid

Publisher: Elsevier

Published: 2014-05-10

Total Pages: 359

ISBN-13: 1483276120

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Probabilistic Methods in Applied Mathematics, Volume 3 focuses on the influence of the probability theory on the formulation of mathematical models and development of theories in many applied fields. The selection first offers information on statistically well-set Cauchy problems and wave propagation in random anisotropic media. Discussions focus on extension to biaxial anisotropic random media; an effective medium description for a random uniaxial anisotropic medium and the resulting dyadic Green's function; evolution of the spectral matrix measure; and well-set Cauchy problems. The text then examines stochastic processes in heat and mass transport, including mass transport, velocity field, temperature transport, and coupling of mass and heat transport. The manuscript takes a look at the potential theory for Markov chains and stochastic differential games. Topics include formal solutions for some classes of stochastic linear pursuit-evasion games; solution of a stochastic linear pursuit-evasion game with nonrandom controls; problems of potential theory; and hitting distributions. The selection is a vital source of data for mathematicians and researchers interested in the probability theory.

Applications of Green's Functions in Science and Engineering
Applications of Green's Functions in Science and Engineering

Author: Michael D. Greenberg

Publisher: Courier Dover Publications

Published: 2015-08-19

Total Pages: 164

ISBN-13: 0486797961

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In addition to coverage of Green's function, this concise introductory treatment examines boundary value problems, generalized functions, eigenfunction expansions, partial differential equations, and acoustics. Suitable for undergraduate and graduate students. 1971 edition.