Innovative Methods For Numerical Solution Of Partial Differential Equations
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Innovative Methods For Numerical Solutions Of Partial Differential Equations
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Author : P. L. Roe
language : en
Publisher: World Scientific
Release Date : 2002
Innovative Methods For Numerical Solutions Of Partial Differential Equations written by P. L. Roe and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
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.
Partial Differential Equations
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Author : Wolfgang Arendt
language : en
Publisher: Springer Nature
Release Date : 2023-01-01
Partial Differential Equations written by Wolfgang Arendt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Mathematics categories.
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.
Numerical Approximation Of Partial Differential Equations
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Author : E.L. Ortiz
language : en
Publisher: Elsevier
Release Date : 1987-02-01
Numerical Approximation Of Partial Differential Equations written by E.L. Ortiz and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-02-01 with Mathematics categories.
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.
Innovative Methods For Numerical Solution Of Partial Differential Equations
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Author : M M Hafez
language : en
Publisher: World Scientific
Release Date : 2001-12-20
Innovative Methods For Numerical Solution Of Partial Differential Equations written by M M Hafez and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-12-20 with Mathematics categories.
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
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Author : R. M. M. Mattheij
language : en
Publisher: SIAM
Release Date : 2005-01-01
Partial Differential Equations written by R. M. M. Mattheij and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
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 Methods For Partial Differential Equations
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Author : William F. Ames
language : en
Publisher: Academic Press
Release Date : 2014-06-28
Numerical Methods For Partial Differential Equations written by William F. Ames and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requirements, and the danger of extrapolation to nonlinear problems methods used on linear problems. Numerical Methods for Partial Differential Equations, Third Edition reflects the great accomplishments that have taken place in scientific computation in the fifteen years since the Second Edition was published. This new edition is a drastic revision of the previous one, with new material on boundary elements, spectral methods, the methods of lines, and invariant methods. At the same time, the new edition retains the self-contained nature of the older version, and shares the clarity of its exposition and the integrity of its presentation. Material on finite elements and finite differences have been merged, and now constitute equal partners Additional material has been added on boundary elements, spectral methods, the method of lines, and invariant methods References have been updated, and reflect the additional material Self-contained nature of the Second Edition has been maintained Very suitable for PDE courses
Methods For The Numerical Solution Of Partial Differential Equations
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Author : Dale U. von Rosenberg
language : en
Publisher:
Release Date : 1977
Methods For The Numerical Solution Of Partial Differential Equations written by Dale U. von Rosenberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with categories.
Introduction To Numerical Ordinary And Partial Differential Equations Using Matlab
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Author : Alexander Stanoyevitch
language : en
Publisher: John Wiley & Sons
Release Date : 2011-10-14
Introduction To Numerical Ordinary And Partial Differential Equations Using Matlab written by Alexander Stanoyevitch and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-14 with Mathematics categories.
Numerical Methods For Partial Differential Equations
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Author : G. Evans
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Methods For Partial Differential Equations written by G. Evans 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 2012-12-06 with Mathematics categories.
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
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Author : Victor Grigor'e Ganzha
language : en
Publisher: CRC Press
Release Date : 2017-11-22
Numerical Solutions For Partial Differential Equations written by Victor Grigor'e Ganzha and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
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.