Download or read book Solution of a Generalized Diffusion Equation by Difference Methods written by Reginald P. Tewarson and published by . This book was released on 1961 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Mathematics of Diffusion written by John Crank and published by Oxford University Press. This book was released on 1979 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Generalized Difference Methods for Differential Equations written by Ronghua Li and published by CRC Press. This book was released on 2000-01-03 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Finite Difference Computing with PDEs written by Hans Petter Langtangen and published by Springer. This book was released on 2017-06-21 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical Solutions of Diffusion type Equations written by John Loyd Bryan and published by . This book was released on 1969 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Generalized Solutions of Functional Differential Equations written by Joseph Wiener and published by World Scientific. This book was released on 1993 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Numerical Solution for the Diffusion Equation in Hydrogeologic Systems written by Audrey L. Ishii and published by . This book was released on 1989 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Partial Differential and Difference Equations and Simultaneous Systems with Constant or Homogeneous Coefficients written by Luis Manuel Braga da Costa Campos and published by CRC Press. This book was released on 2024-06-07 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Classical Implicit Finite Difference Method for Solving Diffusion Equation written by Martina Shoiw-ling Lee and published by . This book was released on 1970 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Numerical Investigation of Extending Diffusion Theory Codes to Solve the Generalized Diffusion Equation in the Edge Pedestal written by John-Patrick Floyd (II.) and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The presence of a large pinch velocity in the edge pedestal of high confinement (H-mode) tokamak plasmas implies that particle transport in the plasma edge ust be treated by a pinch-diffusion theory, rather than a pure diffusion theory. Momentum balance also requires the inclusion of a pinch term in descriptions of edge article transport. A numerical investigation of solving generalized pinch-diffusion theory using methods extended from the numerical solution methodology of pure iffusion theory has been carried out. The generalized diffusion equation has been numerically integrated using the central finite-difference approximation for the diffusion erm and three finite difference approximations of the pinch term, and then solved using Gauss reduction. The pinch-diffusion relation for the radial particle flux was solved directly and used as a benchmark for the finite-difference algorithm solutions to the generalized diffusion equation. Both equations are solved using several esh pacings, and it is found that a finer mesh spacing will be required in the edge pedestal, where the inward pinch velocity is large in H-mode plasmas, than is necessary or similar accuracy further inward where the pinch velocity diminishes. An expression for the numerical error of various finite-differencing algorithms is presented.
Download or read book Numerical Solution of Differential Equations written by Zhilin Li and published by Cambridge University Press. This book was released on 2017-11-30 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical and concise guide to finite difference and finite element methods. Well-tested MATLAB® codes are available online.
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Download or read book Partially Discrete Numerical Solution of the Generalized Diffusion Equation written by Sam Pierce and published by . This book was released on 1970 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: The document contains a study of the partially discrete numerical solution and its convergence for the diffusion equation with any generalized function initial condition including the delta function. (Author).
Download or read book Difference Methods for Solutions of Problems of Mathematical Physics I written by Nikolaĭ Nikolaevich I︠A︡nenko and published by American Mathematical Soc.. This book was released on 1967 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Continuity of Solution of the Generalized Diffusion Equation written by Marshall Phillip Jones and published by . This book was released on 1966 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Heat Transfer and Fluid Flow written by D. Srinivasacharya and published by Springer. This book was released on 2018-12-13 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises selected papers from the International Conference on Numerical Heat Transfer and Fluid Flow (NHTFF 2018), and presents the latest developments in computational methods in heat and mass transfer. It also discusses numerical methods such as finite element, finite difference, and finite volume applied to fluid flow problems. Providing a good balance between computational methods and analytical results applied to a wide variety of problems in heat transfer, transport and fluid mechanics, the book is a valuable resource for students and researchers working in the field of heat transfer and fluid dynamics.
