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Innovative Methods for Numerical Solutions of Partial Differential Equations

Innovative Methods for Numerical Solutions of Partial Differential Equations Author P. L. Roe
ISBN-10 9789810248109
Release 2002
Pages 382
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This book consists of 20 review articles dedicated to Prof. Philip Roe on the occasion of his 60th birthday and in appreciation of his original contributions to computational fluid dynamics. The articles, written by leading researchers in the field, cover many topics, including theory and applications, algorithm developments and modern computational techniques for industry.



Innovative Methods for Numerical Solution of Partial Differential Equations

Innovative Methods for Numerical Solution of Partial Differential Equations Author M M Hafez
ISBN-10 9789814489591
Release 2001-12-20
Pages 416
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This book consists of 20 review articles dedicated to Prof. Philip Roe on the occasion of his 60th birthday and in appreciation of his original contributions to computational fluid dynamics. The articles, written by leading researchers in the field, cover many topics, including theory and applications, algorithm developments and modern computational techniques for industry. Contents:“A One-Sided View”: The Real Story (B van Leer)Collocated Upwind Schemes for Ideal MHD (K G Powell)The Penultimate Scheme for Systems of Conservation Laws: Finite Difference ENO with Marquina's Flux Splitting (R P Fedkiw et al.)A Finite Element Based Level-Set Method for Multiphase Flows (B Engquist & A-K Tornberg)The GHOST Fluid Method for Viscous Flows (R P Fedkiw & X-D Liu)Factorizable Schemes for the Equations of Fluid Flow (D Sidilkover)Evolution Galerkin Methods as Finite Difference Schemes (K W Morton)Fluctuation Distribution Schemes on Adjustable Meshes for Scalar Hyperbolic Equations (M J Baines)Superconvergent Lift Estimates Through Adjoint Error Analysis (M B Giles & N A Pierce)Somewhere between the Lax–Wendroff and Roe Schemes for Calculating Multidimensional Compressible Flows (A Lerat et al.)Flux Schemes for Solving Nonlinear Systems of Conservation Laws (J M Ghidaglia)A Lax–Wendroff Type Theorem for Residual Schemes (R Abgrall et al.)Kinetic Schemes for Solving Saint–Venant Equations on Unstructured Grids (M O Bristeau & B Perthame)Nonlinear Projection Methods for Multi-Entropies Navier–Stokes Systems (C Berthon & F Coquel)A Hybrid Fluctuation Splitting Scheme for Two-Dimensional Compressible Steady Flows (P De Palma et al.)Some Recent Developments in Kinetic Schemes Based on Least Squares and Entropy Variables (S M Deshpande)Difference Approximation for Scalar Conservation Law. Consistency with Entropy Condition from the Viewpoint of Oleinik's E-Condition (H Aiso)Lessons Learned from the Blast Wave Computation Using Overset Moving Grids: Grid Motion Improves the Resolution (K Fujii) Readership: Researchers and graduate students in numerical and computational mathematics in engineering. Keywords:Numerical Methods;Partial Differential Equations;Computational Fluid Dynamics (CFD);Conservation Laws;Kinetic Schemes;Upwinding



Numerical Approximation of Partial Differential Equations

Numerical Approximation of Partial Differential Equations Author E.L. Ortiz
ISBN-10 0080872441
Release 1987-02-01
Pages 430
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This selection of papers is concerned with problems arising in the numerical solution of differential equations, with an emphasis on partial differential equations. There is a balance between theoretical studies of approximation processes, the analysis of specific numerical techniques and the discussion of their application to concrete problems relevant to engineering and science. Special consideration has been given to innovative numerical techniques and to the treatment of three-dimensional and singular problems. These topics are discussed in several of the invited papers. The contributed papers are divided into five parts: techniques of approximation theory which are basic to the numerical treatment of differential equations; numerical techniques based on discrete processes; innovative methods based on polynomial and rational approximation; variational inequalities, conformal transformation and asymptotic techniques; and applications of differential equations to problems in science and engineering.



Numerical Solution of Partial Differential Equations by the Finite Element Method

Numerical Solution of Partial Differential Equations by the Finite Element Method Author Claes Johnson
ISBN-10 9780486131597
Release 2012-05-23
Pages 288
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An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.



Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB

Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB Author Alexander Stanoyevitch
ISBN-10 9781118031506
Release 2011-10-14
Pages 832
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Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB has been writing in one form or another for most of life. You can find so many inspiration from Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB book for free.



Numerical Solution of Partial Differential Equations

Numerical Solution of Partial Differential Equations Author K. W. Morton
ISBN-10 9781139443203
Release 2005-04-11
Pages
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This is the 2005 second edition of a highly successful and well-respected textbook on the numerical techniques used to solve partial differential equations arising from mathematical models in science, engineering and other fields. The authors maintain an emphasis on finite difference methods for simple but representative examples of parabolic, hyperbolic and elliptic equations from the first edition. However this is augmented by new sections on finite volume methods, modified equation analysis, symplectic integration schemes, convection-diffusion problems, multigrid, and conjugate gradient methods; and several sections, including that on the energy method of analysis, have been extensively rewritten to reflect modern developments. Already an excellent choice for students and teachers in mathematics, engineering and computer science departments, the revised text includes more latest theoretical and industrial developments.



Numerical Methods for Partial Differential Equations

Numerical Methods for Partial Differential Equations Author G. Evans
ISBN-10 9781447103776
Release 2012-12-06
Pages 290
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The subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied. The subject was originally developed by the major names of mathematics, in particular, Leonard Euler and Joseph-Louis Lagrange who studied waves on strings; Daniel Bernoulli and Euler who considered potential theory, with later developments by Adrien-Marie Legendre and Pierre-Simon Laplace; and Joseph Fourier's famous work on series expansions for the heat equation. Many of the greatest advances in modern science have been based on discovering the underlying partial differential equation for the process in question. James Clerk Maxwell, for example, put electricity and magnetism into a unified theory by establishing Maxwell's equations for electromagnetic theory, which gave solutions for prob lems in radio wave propagation, the diffraction of light and X-ray developments. Schrodinger's equation for quantum mechanical processes at the atomic level leads to experimentally verifiable results which have changed the face of atomic physics and chemistry in the 20th century. In fluid mechanics, the Navier Stokes' equations form a basis for huge number-crunching activities associated with such widely disparate topics as weather forecasting and the design of supersonic aircraft. Inevitably the study of partial differential equations is a large undertaking, and falls into several areas of mathematics.



Numerical Methods for Partial Differential Equations

Numerical Methods for Partial Differential Equations Author Sandip Mazumder
ISBN-10 9780128035047
Release 2015-12-01
Pages 484
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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 industry Includes 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 codes Includes 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



Transform Methods for Solving Partial Differential Equations Second Edition

Transform Methods for Solving Partial Differential Equations  Second Edition Author Dean G. Duffy
ISBN-10 1420035142
Release 2004-07-15
Pages 728
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Transform methods provide a bridge between the commonly used method of separation of variables and numerical techniques for solving linear partial differential equations. While in some ways similar to separation of variables, transform methods can be effective for a wider class of problems. Even when the inverse of the transform cannot be found analytically, numeric and asymptotic techniques now exist for their inversion, and because the problem retains some of its analytic aspect, one can gain greater physical insight than typically obtained from a purely numerical approach. Transform Methods for Solving Partial Differential Equations, Second Edition illustrates the use of Laplace, Fourier, and Hankel transforms to solve partial differential equations encountered in science and engineering. The author has expanded the second edition to provide a broader perspective on the applicability and use of transform methods and incorporated a number of significant refinements: New in the Second Edition: · Expanded scope that includes numerical methods and asymptotic techniques for inverting particularly complicated transforms · Discussions throughout the book that compare and contrast transform methods with separation of variables, asymptotic methods, and numerical techniques · Many added examples and exercises taken from a wide variety of scientific and engineering sources · Nearly 300 illustrations--many added to the problem sections to help readers visualize the physical problems · A revised format that makes the book easier to use as a reference: problems are classified according to type of region, type of coordinate system, and type of partial differential equation · Updated references, now arranged by subject instead of listed all together As reflected by the book's organization, content, and many examples, the author's focus remains firmly on applications. While the subject matter is classical, this book gives it a fresh, modern treatment that is exceptionally practical, eminently readable, and especially valuable to anyone solving problems in engineering and the applied sciences.



Partial Differential Equations

Partial Differential Equations Author R. M. M. Mattheij
ISBN-10 9780898715941
Release 2005-01-01
Pages 665
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Textbook with a unique approach that integrates analysis and numerical methods and includes modelling to address real-life problems.



Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations

Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations Author David E. Keyes
ISBN-10 0898712882
Release 1992-01-01
Pages 623
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Papers presented at the May 1991 symposium reflect continuing interest in the role of domain decomposition in the effective utilization of parallel systems; applications in fluid mechanics, structures, biology, and design optimization; and maturation of analysis of elliptic equations, with theoretic



Numerical Solutions for Partial Differential Equations

Numerical Solutions for Partial Differential Equations Author Victor Grigor'e Ganzha
ISBN-10 9781351427500
Release 2017-11-22
Pages 347
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Partial differential equations (PDEs) play an important role in the natural sciences and technology, because they describe the way systems (natural and other) behave. The inherent suitability of PDEs to characterizing the nature, motion, and evolution of systems, has led to their wide-ranging use in numerical models that are developed in order to analyze systems that are not otherwise easily studied. Numerical Solutions for Partial Differential Equations contains all the details necessary for the reader to understand the principles and applications of advanced numerical methods for solving PDEs. In addition, it shows how the modern computer system algebra Mathematica® can be used for the analytic investigation of such numerical properties as stability, approximation, and dispersion.



The Numerical Solution of Ordinary and Partial Differential Equations

The Numerical Solution of Ordinary and Partial Differential Equations Author Granville Sewell
ISBN-10 9789814635110
Release 2014-12-16
Pages 348
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This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. Finite difference methods are introduced and analyzed in the first four chapters, and finite element methods are studied in chapter five. A very general-purpose and widely-used finite element program, PDE2D, which implements many of the methods studied in the earlier chapters, is presented and documented in Appendix A. The book contains the relevant theory and error analysis for most of the methods studied, but also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs (FORTRAN or MATLAB) for solving ordinary and partial differential equations, using both finite differences and finite elements. In addition, they will be able to solve very difficult partial differential equations using the software PDE2D, presented in Appendix A. PDE2D solves very general steady-state, time-dependent and eigenvalue PDE systems, in 1D intervals, general 2D regions, and a wide range of simple 3D regions. Contents:Direct Solution of Linear SystemsInitial Value Ordinary Differential EquationsThe Initial Value Diffusion ProblemThe Initial Value Transport and Wave ProblemsBoundary Value ProblemsThe Finite Element MethodsAppendix A — Solving PDEs with PDE2DAppendix B — The Fourier Stability MethodAppendix C — MATLAB ProgramsAppendix D — Answers to Selected Exercises Readership: Undergraduate, graduate students and researchers. Key Features:The discussion of stability, absolute stability and stiffness in Chapter 1 is clearer than in other textsStudents will actually learn to write programs solving a range of simple PDEs using the finite element method in chapter 5In Appendix A, students will be able to solve quite difficult PDEs, using the author's software package, PDE2D. (a free version is available which solves small to moderate sized problems)Keywords:Differential Equations;Partial Differential Equations;Finite Element Method;Finite Difference Method;Computational Science;Numerical AnalysisReviews: "This book is very well written and it is relatively easy to read. The presentation is clear and straightforward but quite rigorous. This book is suitable for a course on the numerical solution of ODEs and PDEs problems, designed for senior level undergraduate or beginning level graduate students. The numerical techniques for solving problems presented in the book may also be useful for experienced researchers and practitioners both from universities or industry." Andrzej Icha Pomeranian Academy in Słupsk Poland



Numerical Methods for Solving Partial Differential Equations

Numerical Methods for Solving Partial Differential Equations Author George F. Pinder
ISBN-10 9781119316381
Release 2018-02-05
Pages 320
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A comprehensive guide to numerical methods for simulating physical-chemical systems This book offers a systematic, highly accessible presentation of numerical methods used to simulate the behavior of physical-chemical systems. Unlike most books on the subject, it focuses on methodology rather than specific applications. Written for students and professionals across an array of scientific and engineering disciplines and with varying levels of experience with applied mathematics, it provides comprehensive descriptions of numerical methods without requiring an advanced mathematical background. Based on its author’s more than forty years of experience teaching numerical methods to engineering students, Numerical Methods for Solving Partial Differential Equations presents the fundamentals of all of the commonly used numerical methods for solving differential equations at a level appropriate for advanced undergraduates and first-year graduate students in science and engineering. Throughout, elementary examples show how numerical methods are used to solve generic versions of equations that arise in many scientific and engineering disciplines. In writing it, the author took pains to ensure that no assumptions were made about the background discipline of the reader. Covers the spectrum of numerical methods that are used to simulate the behavior of physical-chemical systems that occur in science and engineering Written by a professor of engineering with more than forty years of experience teaching numerical methods to engineers Requires only elementary knowledge of differential equations and matrix algebra to master the material Designed to teach students to understand, appreciate and apply the basic mathematics and equations on which Mathcad and similar commercial software packages are based Comprehensive yet accessible to readers with limited mathematical knowledge, Numerical Methods for Solving Partial Differential Equations is an excellent text for advanced undergraduates and first-year graduate students in the sciences and engineering. It is also a valuable working reference for professionals in engineering, physics, chemistry, computer science, and applied mathematics.



Partial Differential Equations

Partial Differential Equations Author Mark S. Gockenbach
ISBN-10 9780898719352
Release 2010-12-02
Pages 654
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A fresh, forward-looking undergraduate textbook that treats the finite element method and classical Fourier series method with equal emphasis.



The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations

The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations Author A. K. Aziz
ISBN-10 9781483267982
Release 2014-05-10
Pages 796
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The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations is a collection of papers presented at the 1972 Symposium by the same title, held at the University of Maryland, Baltimore County Campus. This symposium relates considerable numerical analysis involved in research in both theoretical and practical aspects of the finite element method. This text is organized into three parts encompassing 34 chapters. Part I focuses on the mathematical foundations of the finite element method, including papers on theory of approximation, variational principles, the problems of perturbations, and the eigenvalue problem. Part II covers a large number of important results of both a theoretical and a practical nature. This part discusses the piecewise analytic interpolation and approximation of triangulated polygons; the Patch test for convergence of finite elements; solutions for Dirichlet problems; variational crimes in the field; and superconvergence result for the approximate solution of the heat equation by a collocation method. Part III explores the many practical aspects of finite element method. This book will be of great value to mathematicians, engineers, and physicists.



Computational Partial Differential Equations Using MATLAB

Computational Partial Differential Equations Using MATLAB Author Jichun Li
ISBN-10 1420089056
Release 2008-10-20
Pages 378
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This textbook introduces several major numerical methods for solving various partial differential equations (PDEs) in science and engineering, including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques that include the classic finite difference method and the finite element method as well as state-of-the-art numerical methods, such as the high-order compact difference method and the radial basis function meshless method. Helps Students Better Understand Numerical Methods through Use of MATLAB® The authors uniquely emphasize both theoretical numerical analysis and practical implementation of the algorithms in MATLAB, making the book useful for students in computational science and engineering. They provide students with simple, clear implementations instead of sophisticated usages of MATLAB functions. All the Material Needed for a Numerical Analysis Course Based on the authors’ own courses, the text only requires some knowledge of computer programming, advanced calculus, and difference equations. It includes practical examples, exercises, references, and problems, along with a solutions manual for qualifying instructors. Students can download MATLAB code from www.crcpress.com, enabling them to easily modify or improve the codes to solve their own problems.