Difference Matrices For Ode And Pde
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Difference Matrices For Ode And Pde
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Author : John M. Neuberger
language : en
Publisher: Springer Nature
Release Date : 2023-01-19
Difference Matrices For Ode And Pde written by John M. Neuberger and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-19 with Mathematics categories.
The use of difference matrices and high-level MATLAB® commands to implement finite difference algorithms is pedagogically novel. This unique and concise textbook gives the reader easy access and a general ability to use first and second difference matrices to set up and solve linear and nonlinear systems in MATLAB which approximate ordinary and partial differential equations. Prerequisites include a knowledge of basic calculus, linear algebra, and ordinary differential equations. Some knowledge of partial differential equations is a plus though the text may easily serve as a supplement for the student currently working through an introductory PDEs course. Familiarity with MATLAB is not required though a little prior experience with programming would be helpful. In addition to its special focus on solving in MATLAB, the abundance of examples and exercises make this text versatile in use. It would serve well in a graduate course in introductory scientific computing for partial differential equations. With prerequisites mentioned above plus some elementary numerical analysis, most of the material can be covered and many of the exercises assigned in a single semester course. Some of the more challenging exercises make substantial projects and relate to topics from other typical graduate mathematics courses, e.g., linear algebra, differential equations, or topics in nonlinear functional analysis. A selection of the exercises may be assigned as projects throughout the semester. The student will develop the skills to run simulations corresponding to the primarily theoretical course material covered by the instructor. The book can serve as a supplement for the instructor teaching any course in differential equations. Many of the examples can be easily implemented and the resulting simulation demonstrated by the instructor. If the course has a numerical component, a few of the more difficult exercises may be assigned as student projects. Established researchers in theoretical partial differential equations may find this book useful as well, particularly as an introductory guide for their research students. Those unfamiliar with MATLAB can use the material as a reference to quickly develop their own applications in that language. Practical assistance in implementing algorithms in MATLAB can be found in these pages. A mathematician who is new to the practical implementation of methods for scientific computation in general can learn how to implement and execute numerical simulations of differential equations in MATLAB with relative ease by working through a selection of exercises. Additionally, the book can serve as a practical guide in independent study, undergraduate or graduate research experiences, or for reference in simulating solutions to specific thesis or dissertation-related experiments.
Difference Matrices For Ode And Pde
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Author : John Neuberger
language : en
Publisher:
Release Date : 2023
Difference Matrices For Ode And Pde written by John Neuberger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Difference equations categories.
Finite Difference Methods For Ordinary And Partial Differential Equations
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Author : Randall J. LeVeque
language : en
Publisher: SIAM
Release Date : 2007-09-06
Finite Difference Methods For Ordinary And Partial Differential Equations written by Randall J. LeVeque and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-06 with Mathematics categories.
Introductory textbook from which students can approach more advance topics relating to finite difference methods.
Simulation Of Ode Pde Models With Matlab Octave And Scilab
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Author : Alain Vande Wouwer
language : en
Publisher: Springer
Release Date : 2014-06-07
Simulation Of Ode Pde Models With Matlab Octave And Scilab written by Alain Vande Wouwer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-07 with Technology & Engineering categories.
Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB shows the reader how to exploit a fuller array of numerical methods for the analysis of complex scientific and engineering systems than is conventionally employed. The book is dedicated to numerical simulation of distributed parameter systems described by mixed systems of algebraic equations, ordinary differential equations (ODEs) and partial differential equations (PDEs). Special attention is paid to the numerical method of lines (MOL), a popular approach to the solution of time-dependent PDEs, which proceeds in two basic steps: spatial discretization and time integration. Besides conventional finite-difference and element techniques, more advanced spatial-approximation methods are examined in some detail, including nonoscillatory schemes and adaptive-grid approaches. A MOL toolbox has been developed within MATLAB®/OCTAVE/SCILAB. In addition to a set of spatial approximations and time integrators, this toolbox includes a collection of application examples, in specific areas, which can serve as templates for developing new programs. Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB provides a practical introduction to some advanced computational techniques for dynamic system simulation, supported by many worked examples in the text, and a collection of codes available for download from the book’s page at www.springer.com. This text is suitable for self-study by practicing scientists and engineers and as a final-year undergraduate course or at the graduate level.
Fundamental Algorithms In Computational Fluid Dynamics
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Author : Thomas H. Pulliam
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-03-31
Fundamental Algorithms In Computational Fluid Dynamics written by Thomas H. Pulliam and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-31 with Technology & Engineering categories.
Intended as a textbook for courses in computational fluid dynamics at the senior undergraduate or graduate level, this book is a follow-up to the book Fundamentals of Computational Fluid Dynamics by the same authors, which was published in the series Scientific Computation in 2001. Whereas the earlier book concentrated on the analysis of numerical methods applied to model equations, this new book concentrates on algorithms for the numerical solution of the Euler and Navier-Stokes equations. It focuses on some classical algorithms as well as the underlying ideas based on the latest methods. A key feature of the book is the inclusion of programming exercises at the end of each chapter based on the numerical solution of the quasi-one-dimensional Euler equations and the shock-tube problem. These exercises can be included in the context of a typical course and sample solutions are provided in each chapter, so readers can confirm that they have coded the algorithms correctly.
Emerging Applications Of Control And Systems Theory
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Author : Roberto Tempo
language : en
Publisher: Springer
Release Date : 2018-02-24
Emerging Applications Of Control And Systems Theory written by Roberto Tempo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-24 with Technology & Engineering categories.
This book celebrates Professor Mathukumalli Vidyasagar’s outstanding achievements in systems, control, robotics, statistical learning, computational biology, and allied areas. The contributions in the book summarize the content of invited lectures given at the workshop “Emerging Applications of Control and Systems Theory” (EACST17) held at the University of Texas at Dallas in late September 2017 in honor of Professor Vidyasagar’s seventieth birthday. These contributions are the work of twenty-eight distinguished speakers from eight countries and are related to Professor Vidyasagar’s areas of research. This Festschrift volume will remain as a permanent scientific record of this event.
Optimization In Food Engineering
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Author : Ferruh Erdogdu
language : en
Publisher: CRC Press
Release Date : 2008-12-09
Optimization In Food Engineering written by Ferruh Erdogdu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-09 with Science categories.
While mathematically sophisticated methods can be used to better understand and improve processes, the nonlinear nature of food processing models can make their dynamic optimization a daunting task. With contributions from a virtual who's who in the food processing industry, Optimization in Food Engineering evaluates the potential uses and limitati
Kernel Based Approximation Methods Using Matlab
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Author : Gregory E Fasshauer
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-07-30
Kernel Based Approximation Methods Using Matlab written by Gregory E Fasshauer and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-30 with Mathematics categories.
In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.
Operator Methods For Boundary Value Problems
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Author : Seppo Hassi
language : en
Publisher: Cambridge University Press
Release Date : 2012-10-11
Operator Methods For Boundary Value Problems written by Seppo Hassi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-11 with Mathematics categories.
Presented in this volume are a number of new results concerning the extension theory and spectral theory of unbounded operators using the recent notions of boundary triplets and boundary relations. This approach relies on linear single-valued and multi-valued maps, isometric in a Krein space sense, and offers a basic framework for recent developments in system theory. Central to the theory are analytic tools such as Weyl functions, including Titchmarsh-Weyl m-functions and Dirichlet-to-Neumann maps. A wide range of topics is considered in this context from the abstract to the applied, including boundary value problems for ordinary and partial differential equations; infinite-dimensional perturbations; local point-interactions; boundary and passive control state/signal systems; extension theory of accretive, sectorial and symmetric operators; and Calkin's abstract boundary conditions. This accessible treatment of recent developments, written by leading researchers, will appeal to a broad range of researchers, students and professionals.
Introduction To Finite Element Analysis For Engineers
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Author : Saad A. Ragab
language : en
Publisher: CRC Press
Release Date : 2018-04-17
Introduction To Finite Element Analysis For Engineers written by Saad A. Ragab and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-17 with Technology & Engineering categories.
Finite Element Analysis for Engineers introduces FEA as a technique for solving differential equations, and for application to problems in Civil, Mechanical, Aerospace and Biomedical Engineering and Engineering Science & Mechanics. Intended primarily for senior and first-year graduate students, the text is mathematically rigorous, but in line with students' math courses. Organized around classes of differential equations, the text includes MATLAB code for selected examples and problems. Both solid mechanics and thermal/fluid problems are considered. Based on the first author's class-tested notes, the text builds a solid understanding of FEA concepts and modern engineering applications.