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Author : Abdul Q. M. Khaliq
Publisher :
Page : 256 pages
File Size : 11,61 MB
Release : 2016
Category : Differential equations, Partial
ISBN :
Author : Xiaobing Feng
Publisher : American Mathematical Soc.
Page : 194 pages
File Size : 50,43 MB
Release : 2002
Category : Mathematics
ISBN : 082182970X
This book is derived from lectures presented at the 2001 John H. Barrett Memorial Lectures at the University of Tennessee, Knoxville. The topic was computational mathematics, focusing on parallel numerical algorithms for partial differential equations, their implementation and applications in fluid mechanics and material science. Compiled here are articles from six of nine speakers. Each of them is a leading researcher in the field of computational mathematics and its applications. A vast area that has been coming into its own over the past 15 years, computational mathematics has experienced major developments in both algorithmic advances and applications to other fields. These developments have had profound implications in mathematics, science, engineering and industry. With the aid of powerful high performance computers, numerical simulation of physical phenomena is the only feasible method for analyzing many types of important phenomena, joining experimentation and theoretical analysis as the third method of scientific investigation. The three aspects: applications, theory, and computer implementation comprise a comprehensive overview of the topic. Leading lecturers were Mary Wheeler on applications, Jinchao Xu on theory, and David Keyes on computer implementation. Following the tradition of the Barrett Lectures, these in-depth articles and expository discussions make this book a useful reference for graduate students as well as the many groups of researchers working in advanced computations, including engineering and computer scientists.
Author : María Luz Muñoz-Ruiz
Publisher : Springer Nature
Page : 269 pages
File Size : 17,76 MB
Release : 2021-05-25
Category : Mathematics
ISBN : 3030728501
The present volume contains selected papers issued from the sixth edition of the International Conference "Numerical methods for hyperbolic problems" that took place in 2019 in Málaga (Spain). NumHyp conferences, which began in 2009, focus on recent developments and new directions in the field of numerical methods for hyperbolic partial differential equations (PDEs) and their applications. The 11 chapters of the book cover several state-of-the-art numerical techniques and applications, including the design of numerical methods with good properties (well-balanced, asymptotic-preserving, high-order accurate, domain invariant preserving, uncertainty quantification, etc.), applications to models issued from different fields (Euler equations of gas dynamics, Navier-Stokes equations, multilayer shallow-water systems, ideal magnetohydrodynamics or fluid models to simulate multiphase flow, sediment transport, turbulent deflagrations, etc.), and the development of new nonlinear dispersive shallow-water models. The volume is addressed to PhD students and researchers in Applied Mathematics, Fluid Mechanics, or Engineering whose investigation focuses on or uses numerical methods for hyperbolic systems. It may also be a useful tool for practitioners who look for state-of-the-art methods for flow simulation.
Author : Juan Luis García Guirao
Publisher : Springer
Page : 244 pages
File Size : 34,58 MB
Release : 2019-01-04
Category : Mathematics
ISBN : 3030003418
This work gathers a selection of outstanding papers presented at the 25th Conference on Differential Equations and Applications / 15th Conference on Applied Mathematics, held in Cartagena, Spain, in June 2017. It supports further research into both ordinary and partial differential equations, numerical analysis, dynamical systems, control and optimization, trending topics in numerical linear algebra, and the applications of mathematics to industry. The book includes 14 peer-reviewed contributions and mainly addresses researchers interested in the applications of mathematics, especially in science and engineering. It will also greatly benefit PhD students in applied mathematics, engineering and physics.
Author : George D. Byrne
Publisher : World Scientific
Page : 226 pages
File Size : 31,53 MB
Release : 1992
Category : Mathematics
ISBN : 9789810205577
Ordinary differential equations (ODEs), differential-algebraic equations (DAEs) and partial differential equations (PDEs) are among the forms of mathematics most widely used in science and engineering. Each of these equation types is a focal point for international collaboration and research. This book contains papers by recognized numerical analysts who have made important contributions to the solution of differential systems in the context of realistic applications, and who now report the latest results of their work in numerical methods and software for ODEs/DAEs/PDEs. The papers address parallelization and vectorization of numerical methods, the numerical solution of ODEs/DAEs/PDEs, and the use of these numerical methods in realistic scientific and engineering applications.
Author : Vitoriano Ruas
Publisher : John Wiley & Sons
Page : 376 pages
File Size : 49,36 MB
Release : 2016-04-28
Category : Technology & Engineering
ISBN : 1119111366
Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universités, UPMC - Université Paris 6, France A comprehensive overview of techniques for the computational solution of PDE's Numerical Methods for Partial Differential Equations: An Introduction covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method. The book combines clear descriptions of the three methods, their reliability, and practical implementation aspects. Justifications for why numerical methods for the main classes of PDE's work or not, or how well they work, are supplied and exemplified. Aimed primarily at students of Engineering, Mathematics, Computer Science, Physics and Chemistry among others this book offers a substantial insight into the principles numerical methods in this class of problems are based upon. The book can also be used as a reference for research work on numerical methods for PDE’s. Key features: A balanced emphasis is given to both practical considerations and a rigorous mathematical treatment The reliability analyses for the three methods are carried out in a unified framework and in a structured and visible manner, for the basic types of PDE's Special attention is given to low order methods, as practitioner's overwhelming default options for everyday use New techniques are employed to derive known results, thereby simplifying their proof Supplementary material is available from a companion website.
Author : G. Evans
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 25,32 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1447103793
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.
Author : G. Evans
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 24,63 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1447103777
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.
Author : Cedric Taylor
Publisher :
Page : 426 pages
File Size : 39,47 MB
Release : 1980
Category : Mathematics
ISBN :
Author : L. Lapidus
Publisher : Elsevier
Page : 304 pages
File Size : 46,98 MB
Release : 2014-05-12
Category : Mathematics
ISBN : 148326985X
Numerical Methods for Differential Systems: Recent Developments in Algorithms, Software, and Applications reviews developments in algorithms, software, and applications of numerical methods for differential systems. Topics covered include numerical algorithms for ordinary and partial differential equations (ODE/PDEs); theoretical approaches to the solution of nonlinear algebraic and boundary value problems via associated differential systems; integration algorithms for initial-value ODEs with particular emphasis on stiff systems; finite difference algorithms; and general- and special-purpose computer codes for ODE/PDEs. Comprised of 15 chapters, this book begins with an introduction to high-order A-stable averaging algorithms for stiff differential systems, followed by a discussion on second derivative multistep formulas based on g-splines; numerical integration of linearized stiff ODEs; and numerical solution of large systems of stiff ODEs in a modular simulation framework. Subsequent chapters focus on numerical methods for mass action kinetics; a systematized collection of codes for solving two-point boundary value problems; general software for PDEs; and the choice of algorithms in automated method of lines solution of PDEs. The final chapter is devoted to quality software for ODEs. This monograph should be of interest to mathematicians, chemists, and chemical engineers.