Author: Robert Daniel Carmichael
Publisher:
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 52
Book Description
Linear Difference Equations and Their Analytic Solutions
Author: Robert Daniel Carmichael
Publisher:
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 52
Book Description
Publisher:
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 52
Book Description
Differential-Difference Equations
Author: Bellman
Publisher: Academic Press
ISBN: 0080955142
Category : Mathematics
Languages : en
Pages : 484
Book Description
Differential-Difference Equations
Publisher: Academic Press
ISBN: 0080955142
Category : Mathematics
Languages : en
Pages : 484
Book Description
Differential-Difference Equations
Analytic Solutions of Functional Equations
Author: Sui Sun Cheng
Publisher: World Scientific
ISBN: 9812793348
Category : Mathematics
Languages : en
Pages : 296
Book Description
This book presents a self-contained and unified introduction to the properties of analytic functions. Based on recent research results, it provides many examples of functional equations to show how analytic solutions can be found.Unlike in other books, analytic functions are treated here as those generated by sequences with positive radii of convergence. By developing operational means for handling sequences, functional equations can then be transformed into recurrence relations or difference equations in a straightforward manner. Their solutions can also be found either by qualitative means or by computation. The subsequent formal power series function can then be asserted as a true solution once convergence is established by various convergence tests and majorization techniques. Functional equations in this book may also be functional differential equations or iterative equations, which are different from the differential equations studied in standard textbooks since composition of known or unknown functions are involved.
Publisher: World Scientific
ISBN: 9812793348
Category : Mathematics
Languages : en
Pages : 296
Book Description
This book presents a self-contained and unified introduction to the properties of analytic functions. Based on recent research results, it provides many examples of functional equations to show how analytic solutions can be found.Unlike in other books, analytic functions are treated here as those generated by sequences with positive radii of convergence. By developing operational means for handling sequences, functional equations can then be transformed into recurrence relations or difference equations in a straightforward manner. Their solutions can also be found either by qualitative means or by computation. The subsequent formal power series function can then be asserted as a true solution once convergence is established by various convergence tests and majorization techniques. Functional equations in this book may also be functional differential equations or iterative equations, which are different from the differential equations studied in standard textbooks since composition of known or unknown functions are involved.
Analysis of Finite Difference Schemes
Author: Boško S. Jovanović
Publisher: Springer Science & Business Media
ISBN: 1447154606
Category : Mathematics
Languages : en
Pages : 416
Book Description
This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions. Finite difference methods are a classical class of techniques for the numerical approximation of partial differential equations. Traditionally, their convergence analysis presupposes the smoothness of the coefficients, source terms, initial and boundary data, and of the associated solution to the differential equation. This then enables the application of elementary analytical tools to explore their stability and accuracy. The assumptions on the smoothness of the data and of the associated analytical solution are however frequently unrealistic. There is a wealth of boundary – and initial – value problems, arising from various applications in physics and engineering, where the data and the corresponding solution exhibit lack of regularity. In such instances classical techniques for the error analysis of finite difference schemes break down. The objective of this book is to develop the mathematical theory of finite difference schemes for linear partial differential equations with nonsmooth solutions. Analysis of Finite Difference Schemes is aimed at researchers and graduate students interested in the mathematical theory of numerical methods for the approximate solution of partial differential equations.
Publisher: Springer Science & Business Media
ISBN: 1447154606
Category : Mathematics
Languages : en
Pages : 416
Book Description
This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions. Finite difference methods are a classical class of techniques for the numerical approximation of partial differential equations. Traditionally, their convergence analysis presupposes the smoothness of the coefficients, source terms, initial and boundary data, and of the associated solution to the differential equation. This then enables the application of elementary analytical tools to explore their stability and accuracy. The assumptions on the smoothness of the data and of the associated analytical solution are however frequently unrealistic. There is a wealth of boundary – and initial – value problems, arising from various applications in physics and engineering, where the data and the corresponding solution exhibit lack of regularity. In such instances classical techniques for the error analysis of finite difference schemes break down. The objective of this book is to develop the mathematical theory of finite difference schemes for linear partial differential equations with nonsmooth solutions. Analysis of Finite Difference Schemes is aimed at researchers and graduate students interested in the mathematical theory of numerical methods for the approximate solution of partial differential equations.
Linear Difference Equations and Their Analytic Solutions
Author: Robert Daniel Carmichael
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
The Solutions of Non-homogeneous Linear Difference Equations and Their Asymptotic Form
Author: Kenneth Powers Williams
Publisher:
ISBN:
Category : Difference equations
Languages : en
Pages : 44
Book Description
Publisher:
ISBN:
Category : Difference equations
Languages : en
Pages : 44
Book Description
Finite Difference Methods for Ordinary and Partial Differential Equations
Author: Randall J. LeVeque
Publisher: SIAM
ISBN: 9780898717839
Category : Mathematics
Languages : en
Pages : 356
Book Description
This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Publisher: SIAM
ISBN: 9780898717839
Category : Mathematics
Languages : en
Pages : 356
Book Description
This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Methods of Applied Mathematics for Engineers and Scientists
Author: Tomas B. Co
Publisher: Cambridge University Press
ISBN: 1107004128
Category : Mathematics
Languages : en
Pages : 585
Book Description
This engineering mathematics textbook is rich with examples, applications and exercises, and emphasises applying matrices.
Publisher: Cambridge University Press
ISBN: 1107004128
Category : Mathematics
Languages : en
Pages : 585
Book Description
This engineering mathematics textbook is rich with examples, applications and exercises, and emphasises applying matrices.
American Journal of Mathematics
Author:
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 462
Book Description
The American Journal of Mathematics publishes research papers and articles of broad appeal covering the major areas of contemporary mathematics.
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 462
Book Description
The American Journal of Mathematics publishes research papers and articles of broad appeal covering the major areas of contemporary mathematics.
Science
Author: John Michels (Journalist)
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 990
Book Description
Since Jan. 1901 the official proceedings and most of the papers of the American Association for the Advancement of Science have been included in Science.
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 990
Book Description
Since Jan. 1901 the official proceedings and most of the papers of the American Association for the Advancement of Science have been included in Science.