The Solution Of Initial Value Problems Using Interval Arithmetic
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Solution Of Initial Value Problems In Classes Of Generalized Analytic Functions
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Author : Wolfgang Tutschke
language : en
Publisher: Springer
Release Date : 1989-03-30
Solution Of Initial Value Problems In Classes Of Generalized Analytic Functions written by Wolfgang Tutschke and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-03-30 with Mathematics categories.
The purpose of the present book is to solve initial value problems in classes of generalized analytic functions as well as to explain the functional-analytic background material in detail. From the point of view of the theory of partial differential equations the book is intend ed to generalize the classicalCauchy-Kovalevskayatheorem, whereas the functional-analytic background connected with the method of successive approximations and the contraction-mapping principle leads to the con cept of so-called scales of Banach spaces: 1. The method of successive approximations allows to solve the initial value problem du CTf = f(t,u), (0. 1) u(O) = u , (0. 2) 0 where u = u(t) ist real o. r vector-valued. It is well-known that this method is also applicable if the function u belongs to a Banach space. A completely new situation arises if the right-hand side f(t,u) of the differential equation (0. 1) depends on a certain derivative Du of the sought function, i. e. , the differential equation (0,1) is replaced by the more general differential equation du dt = f(t,u,Du), (0. 3) There are diff. erential equations of type (0. 3) with smooth right-hand sides not possessing any solution to say nothing about the solvability of the initial value problem (0,3), (0,2), Assume, for instance, that the unknown function denoted by w is complex-valued and depends not only on the real variable t that can be interpreted as time but also on spacelike variables x and y, Then the differential equation (0.
The Solution Of Initial Value Problems Using Interval Arithmetic
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Author : P. Eijgenraam
language : en
Publisher:
Release Date : 1963
The Solution Of Initial Value Problems Using Interval Arithmetic written by P. Eijgenraam and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Initial value problems categories.
The Solution Of Initial Value Problems Using Interval Arithmeti
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Author : Pieter Eijgenraam
language : en
Publisher:
Release Date : 1981
The Solution Of Initial Value Problems Using Interval Arithmeti written by Pieter Eijgenraam and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Methods And Applications Of Interval Analysis
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Author : Ramon E. Moore
language : en
Publisher: SIAM
Release Date : 1979-01-01
Methods And Applications Of Interval Analysis written by Ramon E. Moore and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-01-01 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.
Introduction To Interval Analysis
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Author : Ramon E. Moore
language : en
Publisher: SIAM
Release Date : 2009-01-01
Introduction To Interval Analysis written by Ramon E. Moore and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-01 with Mathematics categories.
An update on the author's previous books, this introduction to interval analysis provides an introduction to INTLAB, a high-quality, comprehensive MATLAB toolbox for interval computations, making this the first interval analysis book that does with INTLAB what general numerical analysis texts do with MATLAB.
The Solution Of Initial Value Problems Using Interval Arithmetic
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Author : P. Eijgenraam
language : en
Publisher:
Release Date : 1981
The Solution Of Initial Value Problems Using Interval Arithmetic written by P. Eijgenraam and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Algorithms categories.
Interval Analysis
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Author : Ramon E. Moore
language : en
Publisher:
Release Date : 1966
Interval Analysis written by Ramon E. Moore and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Computer programming categories.
Numerical Solution Of Ordinary Differential Equations
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Author : L.F. Shampine
language : en
Publisher: Routledge
Release Date : 2018-10-24
Numerical Solution Of Ordinary Differential Equations written by L.F. Shampine and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-24 with Mathematics categories.
This new work is an introduction to the numerical solution of the initial value problem for a system of ordinary differential equations. The first three chapters are general in nature, and chapters 4 through 8 derive the basic numerical methods, prove their convergence, study their stability and consider how to implement them effectively. The book focuses on the most important methods in practice and develops them fully, uses examples throughout, and emphasizes practical problem-solving methods.
Interval Arithmetic With Some Applications For Digital Computers
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Author : Sidney Shayer
language : en
Publisher:
Release Date : 1965
Interval Arithmetic With Some Applications For Digital Computers written by Sidney Shayer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Error analysis (Mathematics) categories.
The purpose of this paper is to present a proposed solution to the problem of finding rigorous error bounds, by the use of interval arithmetic. Interval arithmetic is a method of computation in which the rational operations on real numbers are replaced by corresponding operations on closed intervals. That such a replacement is always possible is shown. A discussion is given of interval arithmetic as a system - definitions, operations, theorems, and elementary consequences. An algorithm is presented for the computation of certain functions by the Taylor series, and which has error bounds built into the algorithm. Finally, closed intervals are employed to solve the initial-value first-order differential equation dy dx = f(x, y).
Numerical Methods For Ordinary Differential Equations
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Author : David F. Griffiths
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-11
Numerical Methods For Ordinary Differential Equations written by David F. Griffiths and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-11 with Mathematics categories.
Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject. It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples. Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors. The book covers key foundation topics: o Taylor series methods o Runge--Kutta methods o Linear multistep methods o Convergence o Stability and a range of modern themes: o Adaptive stepsize selection o Long term dynamics o Modified equations o Geometric integration o Stochastic differential equations The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com