Innovative Methods For Numerical Solutions Of Partial Differential Equations
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Innovative Methods for Numerical Solutions of Partial Differential Equations by P. L. Roe,J. J. Chattot Pdf
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 by M M Hafez,J J Chattot Pdf
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
Partial Differential Equations by Wolfgang Arendt,Karsten Urban Pdf
This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach. A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses on finite difference and finite element methods. Computer-aided calculation with MapleTM completes the book. Throughout, three fundamental examples are studied with different tools: Poisson’s equation, the heat equation, and the wave equation on Euclidean domains. The Black–Scholes equation from mathematical finance is one of several opportunities for extension. Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed.
R. M. M. Mattheij,S. W. Rienstra,J. H. M. ten Thije Boonkkamp
Author : R. M. M. Mattheij,S. W. Rienstra,J. H. M. ten Thije Boonkkamp Publisher : SIAM Page : 697 pages File Size : 43,5 Mb Release : 2005-01-01 Category : Mathematics ISBN : 0898718279
Partial Differential Equations by R. M. M. Mattheij,S. W. Rienstra,J. H. M. ten Thije Boonkkamp Pdf
Partial differential equations (PDEs) are used to describe a large variety of physical phenomena, from fluid flow to electromagnetic fields, and are indispensable to such disparate fields as aircraft simulation and computer graphics. While most existing texts on PDEs deal with either analytical or numerical aspects of PDEs, this innovative and comprehensive textbook features a unique approach that integrates analysis and numerical solution methods and includes a third component - modeling - to address real-life problems. The authors believe that modeling can be learned only by doing; hence a separate chapter containing 16 user-friendly case studies of elliptic, parabolic, and hyperbolic equations is included and numerous exercises are included in all other chapters.
Numerical Approximation of Partial Differential Equations by E.L. Ortiz Pdf
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 Methods for Partial Differential Equations by William F. Ames Pdf
Numerical Methods for Partial Differential Equations, Second Edition deals with the use of numerical methods to solve partial differential equations. In addition to numerical fluid mechanics, hopscotch and other explicit-implicit methods are also considered, along with Monte Carlo techniques, lines, fast Fourier transform, and fractional steps methods. Comprised of six chapters, this volume begins with an introduction to numerical calculation, paying particular attention to the classification of equations and physical problems, asymptotics, discrete methods, and dimensionless forms. Subsequent chapters focus on parabolic and hyperbolic equations, elliptic equations, and special topics ranging from singularities and shocks to Navier-Stokes equations and Monte Carlo methods. The final chapter discuss the general concepts of weighted residuals, with emphasis on orthogonal collocation and the Bubnov-Galerkin method. The latter procedure is used to introduce finite elements. This book should be a valuable resource for students and practitioners in the fields of computer science and applied mathematics.
Numerical Methods for Partial Differential Equations by G. Evans,J. Blackledge,P. Yardley Pdf
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 Solutions for Partial Differential Equations by Victor Grigor'e Ganzha,Evgenii Vasilev Vorozhtsov Pdf
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.
Numerical Solutions of Partial Differential Equations by Silvia Bertoluzza,Silvia Falletta,Giovanni Russo,Chi-Wang Shu Pdf
This book presents some of the latest developments in numerical analysis and scientific computing. Specifically, it covers central schemes, error estimates for discontinuous Galerkin methods, and the use of wavelets in scientific computing.
Fractional Partial Differential Equations and Their Numerical Solutions by Boling Guo,Xueke Pu,Fenghui Huang Pdf
This book aims to introduce some new trends and results on the study of the fractional differential equations, and to provide a good understanding of this field to beginners who are interested in this field, which is the authors' beautiful hope. This book describes theoretical and numerical aspects of the fractional partial differential equations, including the authors' researches in this field, such as the fractional Nonlinear Schrödinger equations, fractional Landau–Lifshitz equations and fractional Ginzburg–Landau equations. It also covers enough fundamental knowledge on the fractional derivatives and fractional integrals, and enough background of the fractional PDEs. Contents:Physics BackgroundFractional Calculus and Fractional Differential EquationsFractional Partial Differential EquationsNumerical Approximations in Fractional CalculusNumerical Methods for the Fractional Ordinary Differential EquationsNumerical Methods for Fractional Partial Differential Equations Readership: Graduate students and researchers in mathematical physics, numerical analysis and computational mathematics. Key Features:This book covers the fundamentals of this field, especially for the beginnersThe book covers new trends and results in this fieldThe book covers numerical results, which will be of broad interests to researchersKeywords:Fractional Partial Differential Equations;Numerical Solutions
Computational Fluid Mechanics and Heat Transfer by Dale Anderson,John C. Tannehill,Richard H. Pletcher,Ramakanth Munipalli,Vijaya Shankar Pdf
Computational Fluid Mechanics and Heat Transfer, Fourth Edition is a fully updated version of the classic text on finite-difference and finite-volume computational methods. Divided into two parts, the text covers essential concepts in the first part, and then moves on to fluids equations in the second. Designed as a valuable resource for practitioners and students, new examples and homework problems have been added to further enhance the student’s understanding of the fundamentals and applications. Provides a thoroughly updated presentation of CFD and computational heat transfer Covers more material than other texts, organized for classroom instruction and self-study Presents a wide range of computation strategies for fluid flow and heat transfer Includes new sections on finite element methods, computational heat transfer, and multiphase flows Features a full Solutions Manual and Figure Slides for classroom projection Written as an introductory text for advanced undergraduates and first-year graduate students, the new edition provides the background necessary for solving complex problems in fluid mechanics and heat transfer.
Innovations in Computing Sciences and Software Engineering by Tarek Sobh,Khaled Elleithy Pdf
Innovations in Computing Sciences and Software Engineering includes a set of rigorously reviewed world-class manuscripts addressing and detailing state-of-the-art research projects in the areas of Computer Science, Software Engineering, Computer Engineering, and Systems Engineering and Sciences. Topics Covered: •Image and Pattern Recognition: Compression, Image processing, Signal Processing Architectures, Signal Processing for Communication, Signal Processing Implementation, Speech Compression, and Video Coding Architectures. •Languages and Systems: Algorithms, Databases, Embedded Systems and Applications, File Systems and I/O, Geographical Information Systems, Kernel and OS Structures, Knowledge Based Systems, Modeling and Simulation, Object Based Software Engineering, Programming Languages, and Programming Models and tools. •Parallel Processing: Distributed Scheduling, Multiprocessing, Real-time Systems, Simulation Modeling and Development, and Web Applications. •Signal and Image Processing: Content Based Video Retrieval, Character Recognition, Incremental Learning for Speech Recognition, Signal Processing Theory and Methods, and Vision-based Monitoring Systems. •Software and Systems: Activity-Based Software Estimation, Algorithms, Genetic Algorithms, Information Systems Security, Programming Languages, Software Protection Techniques, Software Protection Techniques, and User Interfaces. •Distributed Processing: Asynchronous Message Passing System, Heterogeneous Software Environments, Mobile Ad Hoc Networks, Resource Allocation, and Sensor Networks. •New trends in computing: Computers for People of Special Needs, Fuzzy Inference, Human Computer Interaction, Incremental Learning, Internet-based Computing Models, Machine Intelligence, Natural Language.
Analytic Methods for Partial Differential Equations by G. Evans,J. Blackledge,P. Yardley Pdf
This is the practical introduction to the analytical approach taken in Volume 2. Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early stage. The characteristic method for first order equations acts as an introduction to the classification of second order quasi-linear problems by characteristics. Attention then moves to different co-ordinate systems, primarily those with cylindrical or spherical symmetry. Hence a discussion of special functions arises quite naturally, and in each case the major properties are derived. The next section deals with the use of integral transforms and extensive methods for inverting them, and concludes with links to the use of Fourier series.
