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Author : Bellman
Publisher : Academic Press
Page : 484 pages
File Size : 25,89 MB
Release : 1963-01-01
Category : Mathematics
ISBN : 0080955142
Differential-Difference Equations
Author : Samuel Goldberg
Publisher : Courier Corporation
Page : 292 pages
File Size : 11,60 MB
Release : 1986-01-01
Category : Mathematics
ISBN : 0486650847
Exceptionally clear exposition of an important mathematical discipline and its applications to sociology, economics, and psychology. Topics include calculus of finite differences, difference equations, matrix methods, and more. 1958 edition.
Author : R Mickens
Publisher : CRC Press
Page : 470 pages
File Size : 27,90 MB
Release : 1991-01-01
Category : Mathematics
ISBN : 9780442001360
In recent years, the study of difference equations has acquired a new significance, due in large part to their use in the formulation and analysis of discrete-time systems, the numerical integration of differential equations by finite-difference schemes, and the study of deterministic chaos. The second edition of Difference Equations: Theory and Applications provides a thorough listing of all major theorems along with proofs. The text treats the case of first-order difference equations in detail, using both analytical and geometrical methods. Both ordinary and partial difference equations are considered, along with a variety of special nonlinear forms for which exact solutions can be determined. Numerous worked examples and problems allow readers to fully understand the material in the text. They also give possible generalization of the theorems and application models. The text's expanded coverage of application helps readers appreciate the benefits of using difference equations in the modeling and analysis of "realistic" problems from a broad range of fields. The second edition presents, analyzes, and discusses a large number of applications from the mathematical, biological, physical, and social sciences. Discussions on perturbation methods and difference equation models of differential equation models of differential equations represent contributions by the author to the research literature. Reference to original literature show how the elementary models of the book can be extended to more realistic situations. Difference Equations, Second Edition gives readers a background in discrete mathematics that many workers in science-oriented industries need as part of their general scientific knowledge. With its minimal mathematical background requirements of general algebra and calculus, this unique volume will be used extensively by students and professional in science and technology, in areas such as applied mathematics, control theory, population science, economics, and electronic circuits, especially discrete signal processing.
Author : Saber N. Elaydi
Publisher : Springer Science & Business Media
Page : 441 pages
File Size : 10,11 MB
Release : 2013-03-14
Category : Mathematics
ISBN : 1475731108
Integrating both classical and modern treatments of difference equations, this book contains the most updated and comprehensive material on stability, Z-transform, discrete control theory, asymptotic theory, continued fractions and orthogonal polynomials. While the presentation is simple enough for use by advanced undergraduates and beginning graduates in mathematics, engineering science, and economics, it will also be a useful reference for scientists and engineers interested in discrete mathematical models. The text covers a large set of applications in a variety of disciplines, including neural networks, feedback control, Markov chains, trade models, heat transfer, propagation of plants, epidemic models and host-parasitoid systems, with each section rounded off by an extensive and highly selected set of exercises.
Author : Glenn Fulford
Publisher : Cambridge University Press
Page : 420 pages
File Size : 10,73 MB
Release : 1997-06-12
Category : Mathematics
ISBN : 9780521446181
Any student wishing to solve problems via mathematical modelling will find that this book provides an excellent introduction to the subject.
Author : Sandra Pinelas
Publisher : Springer Science & Business Media
Page : 639 pages
File Size : 10,8 MB
Release : 2013-09-21
Category : Mathematics
ISBN : 1461473330
The volume contains carefully selected papers presented at the International Conference on Differential & Difference Equations and Applications held in Ponta Delgada – Azores, from July 4-8, 2011 in honor of Professor Ravi P. Agarwal. The objective of the gathering was to bring together researchers in the fields of differential & difference equations and to promote the exchange of ideas and research. The papers cover all areas of differential and difference equations with a special emphasis on applications.
Author : Walter G. Kelley
Publisher : Academic Press
Page : 418 pages
File Size : 49,2 MB
Release : 2001
Category : Mathematics
ISBN : 9780124033306
Difference Equations, Second Edition, presents a practical introduction to this important field of solutions for engineering and the physical sciences. Topic coverage includes numerical analysis, numerical methods, differential equations, combinatorics and discrete modeling. A hallmark of this revision is the diverse application to many subfields of mathematics. Phase plane analysis for systems of two linear equations Use of equations of variation to approximate solutions Fundamental matrices and Floquet theory for periodic systems LaSalle invariance theorem Additional applications: secant line method, Bison problem, juvenile-adult population model, probability theory Appendix on the use of Mathematica for analyzing difference equaitons Exponential generating functions Many new examples and exercises
Author : Randall J. LeVeque
Publisher : SIAM
Page : 356 pages
File Size : 44,33 MB
Release : 2007-01-01
Category : Mathematics
ISBN : 9780898717839
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.
Author : R.P. Agarwal
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 41,22 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 9401715688
The last fifty years have witnessed several monographs and hundreds of research articles on the theory, constructive methods and wide spectrum of applications of boundary value problems for ordinary differential equations. In this vast field of research, the conjugate (Hermite) and the right focal point (Abei) types of problems have received the maximum attention. This is largely due to the fact that these types of problems are basic, in the sense that the methods employed in their study are easily extendable to other types of prob lems. Moreover, the conjugate and the right focal point types of boundary value problems occur frequently in real world problems. In the monograph Boundary Value Problems for Higher Order Differential Equations published in 1986, we addressed the theory of conjugate boundary value problems. At that time the results on right focal point problems were scarce; however, in the last ten years extensive research has been done. In Chapter 1 of the mono graph we offer up-to-date information of this newly developed theory of right focal point boundary value problems. Until twenty years ago Difference Equations were considered as the dis cretizations of the differential equations. Further, it was tacitly taken for granted that the theories of difference and differential equations are parallel. However, striking diversities and wide applications reported in the last two decades have made difference equations one of the major areas of research.
Author : Allaberen Ashyralyev
Publisher : Birkhäuser
Page : 453 pages
File Size : 48,95 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3034879229
This book explores new difference schemes for approximating the solutions of regular and singular perturbation boundary-value problems for PDEs. The construction is based on the exact difference scheme and Taylor's decomposition on the two or three points, which permits investigation of differential equations with variable coefficients and regular and singular perturbation boundary value problems.