Solution of a Generalized Diffusion Equation by Difference Methods PDF Download

Author: Reginald P. Tewarson
Publisher:
ISBN:
Category : Difference equations
Languages : en
Pages : 51

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Author: John Crank
Publisher: Oxford University Press
ISBN: 9780198534112
Category : Mathematics
Languages : en
Pages : 428

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Book Description
Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.

Author: Ronghua Li
Publisher: CRC Press
ISBN: 9780824703301
Category : Mathematics
Languages : en
Pages : 470

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Book Description
This text presents a comprehensive mathematical theory for elliptic, parabolic, and hyperbolic differential equations. It compares finite element and finite difference methods and illustrates applications of generalized difference methods to elastic bodies, electromagnetic fields, underground water pollution, and coupled sound-heat flows.

Author: John Loyd Bryan
Publisher:
ISBN:
Category : Equations
Languages : en
Pages : 106

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Book Description
A method of obtaining numerical solutions of a general class of boundary-value problems governed by the two-dimensional diffusion equation is investigated. The method employs a partial discretization of independent variables to reduce the problem of partial differential equations to a sequence of related boundary-value problems governed by a system of linear second-order ordinary differential equations. The generality of the method is demonstrated by applications to example problems involving both regular and irregular boundaries with boundary conditions of a general type. Application of separation of variables techniques to obtain closed-form solutions of a certain class of problems is presented and the results are used to indicate the accuracy of the method. An investigation into the stability characteristics of the resulting system of ordinary differential equations is also presented. It is concluded that the method appears to show promise as an easily implemented numerical method but that the full potential of the approach will not be realized until significant advances have been made in both computing hardware and software. (Author).

Author: Hans Petter Langtangen
Publisher: Springer
ISBN: 3319554565
Category : Computers
Languages : en
Pages : 522

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Book Description
This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

Author: Randall J. LeVeque
Publisher: SIAM
ISBN: 9780898717839
Category : Mathematics
Languages : en
Pages : 356

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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.

Author: Joseph Wiener
Publisher: World Scientific
ISBN: 9789810212070
Category : Mathematics
Languages : en
Pages : 428

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Book Description
The need to investigate functional differential equations with discontinuous delays is addressed in this book. Recording the work and findings of several scientists on differential equations with piecewise continuous arguments over the last few years, this book serves as a useful source of reference. Great interest is placed on discussing the stability, oscillation and periodic properties of the solutions. Considerable attention is also given to the study of initial and boundary-value problems for partial differential equations of mathematical physics with discontinuous time delays. In fact, a large part of the book is devoted to the exploration of differential and functional differential equations in spaces of generalized functions (distributions) and contains a wealth of new information in this area. Each topic discussed appears to provide ample opportunity for extending the known results. A list of new research topics and open problems is also included as an update.

Author: Luis Manuel Braga da Costa Campos
Publisher: CRC Press
ISBN: 1040010172
Category : Mathematics
Languages : en
Pages : 243

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Book Description
Linear Partial Differential and Difference Equations and Simultaneous Systems: With Constant or Homogeneous Coefficients is part of the series "Mathematics and Physics for Science and Technology," which combines rigorous mathematics with general physical principles to model practical engineering systems with a detailed derivation and interpretation of results. Volume V presents the mathematical theory of partial differential equations and methods of solution satisfying initial and boundary conditions, and includes applications to: acoustic, elastic, water, electromagnetic and other waves; the diffusion of heat, mass, and electricity; and their interactions. This is the third book of the volume. The book starts with six different methods of solution of linear partial differential equations (p.d.e.) with constant coefficients. One of the methods, namely characteristic polynomial, is then extended to a further five classes, including linear p.d.e. with homogeneous power coefficients and finite difference equations and simultaneous systems of both (simultaneous partial differential equations [s.p.d.e.] and simultaneous finite difference equations [s.f.d.e.]). The applications include detailed solutions of the most important p.d.e. in physics and engineering, including the Laplace, heat, diffusion, telegraph, bar, and beam equations. The free and forced solutions are considered together with boundary, initial, asymptotic, starting, and other conditions. The book is intended for graduate students and engineers working with mathematical models and can be applied to problems in mechanical, aerospace, electrical, and other branches of engineering dealing with advanced technology, and also in the physical sciences and applied mathematics.

Author: Martina Shoiw-ling Lee
Publisher:
ISBN:
Category : Diffusion
Languages : en
Pages : 154

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Book Description
This thesis introduces a technique for approximating to a desired degree of accuracy a linear parabolic equation of two spatial dimensions with given initial data and prescribed boundary conditions. The technique is generalized to non-linear parabolic equations. It is stable for all mesh ratios, and it is second order accurate with respect to the spatial variables and first order accurate with respect to the time variable. The method is then applied to the solution of a non-linear diffusion equation describing the flow of a fluid in a saturated, porous medium.

Author: Audrey L. Ishii
Publisher:
ISBN:
Category : Aquifers
Languages : en
Pages : 100

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Book Description