Generalized Difference Methods for Differential Equations, Li, Ronghua
Автор: Strang Название: Differential Equations and Linear Algebra ISBN: 0980232791 ISBN-13(EAN): 9780980232790 Издательство: Cambridge Academ Рейтинг: Цена: 60180.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.
Автор: Oksendal Название: Stochastic Differential Equations ISBN: 3540047581 ISBN-13(EAN): 9783540047582 Издательство: Springer Рейтинг: Цена: 54820.00 T Наличие на складе: Есть Описание: Gives an introduction to the basic theory of stochastic calculus and its applications. This book offers examples in order to motivate and illustrate the theory and show its importance for many applications in for example economics, biology and physics.
Автор: li zhilin Название: Numerical solution of differential equations ISBN: 1107163226 ISBN-13(EAN): 9781107163225 Издательство: Cambridge Academ Рейтинг: Цена: 89760.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This practical and concise guide to finite difference and finite element methods is aimed at graduate students who need to solve differential equations. With few prerequisites, the book is accessible to readers from a range of disciplines across science and engineering. Well-tested MATLAB (R) codes are available online.
Автор: R. M. M. Mattheij Название: Partial Differential Equations ISBN: 0898715946 ISBN-13(EAN): 9780898715941 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 142120.00 T Наличие на складе: Нет в наличии. Описание: Partial differential equations (PDEs) are used to describe a large variety of physical phenomena, from fluid flow to electromagnetic fields, and are indispensable to such disparate fields as aircraft simulation and computer graphics. While most existing texts on PDEs deal with either analytical or numerical aspects of PDEs, this innovative and comprehensive textbook features a unique approach that integrates analysis and numerical solution methods and includes a third component - modeling - to address real-life problems. The authors believe that modeling can be learned only by doing; hence a separate chapter containing 16 user-friendly case studies of elliptic, parabolic, and hyperbolic equations is included and numerous exercises are included in all other chapters.
Автор: Bo?ko S. Jovanovi?, Endre S?li Название: Analysis of Finite Difference Schemes ISBN: 1447154592 ISBN-13(EAN): 9781447154594 Издательство: Springer Рейтинг: Цена: 102480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: 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.
Автор: Bo?ko S. Jovanovi?; Endre S?li Название: Analysis of Finite Difference Schemes ISBN: 1447172590 ISBN-13(EAN): 9781447172598 Издательство: Springer Рейтинг: Цена: 88500.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: 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.
Автор: Randall LeVeque Название: Finite Difference Methods for Ordinary and Partial Differential Equations ISBN: 0898716292 ISBN-13(EAN): 9780898716290 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 67710.00 T Наличие на складе: Нет в наличии. Описание: 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. Exercises and student projects are available on the book’s webpage, along with Matlab mfiles for implementing methods. Readers will gain an understanding of the essential ideas that underlie the development, analysis, and practical use of finite difference methods as well as the key concepts of stability theory, their relation to one another, and their practical implications. The author provides a foundation from which students can approach more advanced topics.
Автор: Sandip Mazumder Название: Numerical Methods for Partial Differential Equations ISBN: 0128498943 ISBN-13(EAN): 9780128498941 Издательство: Elsevier Science Рейтинг: Цена: 114530.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
"Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods" focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. The solution of PDEs can be very challenging, depending on the type of equation, the number of independent variables, the boundary, and initial conditions, and other factors. These two methods have been traditionally used to solve problems involving fluid flow.
For practical reasons, the finite element method, used more often for solving problems in solid mechanics, and covered extensively in various other texts, has been excluded. The book is intended for beginning graduate students and early career professionals, although advanced undergraduate students may find it equally useful.
The material is meant to serve as a prerequisite for students who might go on to take additional courses in computational mechanics, computational fluid dynamics, or computational electromagnetics. The notations, language, and technical jargon used in the book can be easily understood by scientists and engineers who may not have had graduate-level applied mathematics or computer science courses. Presents one of the few available resources that comprehensively describes and demonstrates the finite volume method for unstructured mesh used frequently by practicing code developers in industryIncludes step-by-step algorithms and code snippets in each chapter that enables the reader to make the transition from equations on the page to working codesIncludes 51 worked out examples that comprehensively demonstrate important mathematical steps, algorithms, and coding practices required to numerically solve PDEs, as well as how to interpret the results from both physical and mathematic perspectives
Автор: Smith, G. D. Название: Numerical Solution of Partial Differential Equations ISBN: 0198596502 ISBN-13(EAN): 9780198596509 Издательство: Oxford Academ Рейтинг: Цена: 96090.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolicequations, and a considerably improved presentation of iterative methods. A fast-paced introduction to numerical methods, this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline.
Автор: Leonard C. Maximon Название: Differential and Difference Equations ISBN: 331929735X ISBN-13(EAN): 9783319297354 Издательство: Springer Рейтинг: Цена: 65210.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
Preface.
Introduction.
1 Operators.
2 Solution of homogeneous and inhomogeneous linear equations. 2.1 Variation of constants. 2.2 Reduction of order when one solution to the homogeneous equation is known.
3 First order homogeneous and inhomogeneous linear equations.
4 Second-order homogeneous and inhomogeneous equations.
7 Generating function, z-transforms, Laplace transforms and the solution of linear differential and difference equations. 7.1 Laplace transforms and the solution of linear differential equations with constant coefficients. 7.2 Generating functions and the solution of linear difference equations with constant coefficient. 7.3 Laplace transforms and the solution of linear differential equations with polynomial coefficients. 7.4 Alternative method for the solution of homogeneous linear differential equations with linear coefficients. 7.5 Generating functions and the solution of linear difference equations with polynomial coefficients. 7.6 Solution of homogeneous linear difference equations with linear coefficients.
8 Dictionary of difference equations with polynomial coefficients.
Appendix A: Difference operator.
Appendix B: Notation.
Appendix C: Wronskian Determinant.
Appendix D: Casoratian Determinant.
Appendix E: Cramer's Rule.
Appendix F: Green's function and the Superposition principle.
Appendix G: Inverse Laplace transforms and Inverse Generating functions.
Appendix H: Hypergeometric function.
Appendix I: Confluent Hypergeometric function.
Appendix J. Solutions of the second kind.
Bibliography.
Автор: Guang-hua Gao, Zhi-Zhong Sun Название: Fractional Differential Equations: Finite Difference Methods ISBN: 3110615177 ISBN-13(EAN): 9783110615173 Издательство: Walter de Gruyter Рейтинг: Цена: 140030.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
Starting with an introduction to fractional derivatives and numerical approximations, this book presents finite difference methods for fractional differential equations, including time-fractional sub-diffusion equations, time-fractional wave equations, and space-fractional differential equations, among others. Approximation methods for fractional derivatives are developed and approximate accuracies are analyzed in detail.
2 Solution of homogeneous and inhomogeneous linear equations. 2.1 Variation of constants. 2.2 Reduction of order when one solution to the homogeneous equation is known.
3 First order homogeneous and inhomogeneous linear equations.
4 Second-order homogeneous and inhomogeneous equations.
7 Generating function, z-transforms, Laplace transforms and the solution of linear differential and difference equations. 7.1 Laplace transforms and the solution of linear differential equations with constant coefficients. 7.2 Generating functions and the solution of linear difference equations with constant coefficient. 7.3 Laplace transforms and the solution of linear differential equations with polynomial coefficients. 7.4 Alternative method for the solution of homogeneous linear differential equations with linear coefficients. 7.5 Generating functions and the solution of linear difference equations with polynomial coefficients. 7.6 Solution of homogeneous linear difference equations with linear coefficients.
8 Dictionary of difference equations with polynomial coefficients.
Appendix A: Difference operator.
Appendix B: Notation.
Appendix C: Wronskian Determinant.
Appendix D: Casoratian Determinant.
Appendix E: Cramer's Rule.
Appendix F: Green's function and the Superposition principle.
Appendix G: Inverse Laplace transforms and Inverse Generating functions.
Appendix H: Hypergeometric function.
Appendix I: Confluent Hypergeometric function.
Appendix J. Solutions of the second kind.
Bibliography.
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