Exact Finite-Difference Schemes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Exact Finite-Difference Schemes write by Sergey Lemeshevsky. This book was released on 2016-09-26. Exact Finite-Difference Schemes available in PDF, EPUB and Kindle. Exact Finite-Difference Schemes is a first overview of the topic also describing the state-of-the-art in this field of numerical analysis. Construction of exact difference schemes for various parabolic and elliptic partial differential equations are discussed, including vibrations and transport problems. After this, applications are discussed, such as the discretisation of ODEs and PDEs and numerical methods for stochastic differential equations. Contents: Basic notation Preliminary results Hyperbolic equations Parabolic equations Use of exact difference schemes to construct NSFD discretizations of differential equations Exact and truncated difference schemes for boundary-value problem Exact difference schemes for stochastic differential equations Numerical blow-up time Bibliography
Analysis of Finite Difference Schemes
Analysis of Finite Difference Schemes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analysis of Finite Difference Schemes write by Boško S. Jovanović. This book was released on 2013-10-22. Analysis of Finite Difference Schemes available in PDF, EPUB and Kindle. 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.
Nonstandard Finite Difference Models of Differential Equations
Nonstandard Finite Difference Models of Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonstandard Finite Difference Models of Differential Equations write by Ronald E. Mickens. This book was released on 1994. Nonstandard Finite Difference Models of Differential Equations available in PDF, EPUB and Kindle. This book provides a clear summary of the work of the author on the construction of nonstandard finite difference schemes for the numerical integration of differential equations. The major thrust of the book is to show that discrete models of differential equations exist such that the elementary types of numerical instabilities do not occur. A consequence of this result is that in general bigger step-sizes can often be used in actual calculations and/or finite difference schemes can be constructed that are conditionally stable in many instances whereas in using standard techniques no such schemes exist. The theoretical basis of this work is centered on the concepts of ?exact? and ?best? finite difference schemes. In addition, a set of rules is given for the discrete modeling of derivatives and nonlinear expressions that occur in differential equations. These rules often lead to a unique nonstandard finite difference model for a given differential equation.
Nonstandard Finite Difference Schemes: Methodology And Applications
Nonstandard Finite Difference Schemes: Methodology And Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonstandard Finite Difference Schemes: Methodology And Applications write by Ronald E Mickens. This book was released on 2020-11-11. Nonstandard Finite Difference Schemes: Methodology And Applications available in PDF, EPUB and Kindle. This second edition of Nonstandard Finite Difference Models of Differential Equations provides an update on the progress made in both the theory and application of the NSFD methodology during the past two and a half decades. In addition to discussing details related to the determination of the denominator functions and the nonlocal discrete representations of functions of dependent variables, we include many examples illustrating just how this should be done.Of real value to the reader is the inclusion of a chapter listing many exact difference schemes, and a chapter giving NSFD schemes from the research literature. The book emphasizes the critical roles played by the 'principle of dynamic consistency' and the use of sub-equations for the construction of valid NSFD discretizations of differential equations.
Exact Finite-Difference Schemes
Exact Finite-Difference Schemes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Exact Finite-Difference Schemes write by Sergey Lemeshevsky. This book was released on 2016-09-26. Exact Finite-Difference Schemes available in PDF, EPUB and Kindle. Exact Finite-Difference Schemes is a first overview of the topic also describing the state-of-the-art in this field of numerical analysis. Construction of exact difference schemes for various parabolic and elliptic partial differential equations are discussed, including vibrations and transport problems. After this, applications are discussed, such as the discretisation of ODEs and PDEs and numerical methods for stochastic differential equations. Contents: Basic notation Preliminary results Hyperbolic equations Parabolic equations Use of exact difference schemes to construct NSFD discretizations of differential equations Exact and truncated difference schemes for boundary-value problem Exact difference schemes for stochastic differential equations Numerical blow-up time Bibliography
