Finite Difference Methods for Ordinary and Partial Differential Equations

Steady-State and Time-Dependent Problems

Author: Randall J. LeVeque

Publisher: SIAM

ISBN: 9780898717839

Category: Differential equations

Page: 339

View: 1438

This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

Finite Volume Methods for Hyperbolic Problems

Author: Randall J. LeVeque

Publisher: Cambridge University Press

ISBN: 1139434187

Category: Mathematics

Page: N.A

View: 2661

This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.

High Performance Programming for Soft Computing

Author: Oscar Humberto Montiel Ross,Roberto Sepulveda

Publisher: CRC Press

ISBN: 1466586028

Category: Computers

Page: 376

View: 3880

This book examines the present and future of soft computer techniques. It explains how to use the latest technological tools, such as multicore processors and graphics processing units, to implement highly efficient intelligent system methods using a general purpose computer.

50 Years with Hardy Spaces

A Tribute to Victor Havin

Author: Anton Baranov,Sergei Kisliakov,Nikolai Nikolski

Publisher: Birkhäuser

ISBN: 3319590782

Category: Mathematics

Page: 484

View: 498

Written in honor of Victor Havin (1933–2015), this volume presents a collection of surveys and original papers on harmonic and complex analysis, function spaces and related topics, authored by internationally recognized experts in the fields. It also features an illustrated scientific biography of Victor Havin, one of the leading analysts of the second half of the 20th century and founder of the Saint Petersburg Analysis Seminar. A complete list of his publications, as well as his public speech "Mathematics as a source of certainty and uncertainty", presented at the Doctor Honoris Causa ceremony at Linköping University, are also included.

Random Differential Equations in Scientific Computing

Author: Tobias Neckel,Florian Rupp

Publisher: Walter de Gruyter

ISBN: 8376560263

Category: Mathematics

Page: 650

View: 3989

The book offers a hollistic approach to the theory and numerics of random differential equations from an interdisciplinary and problem-centered point of view. In this interdisciplinary work, the authors examine state–of-the-art concepts of both dynamical systems and scientific computing.

Parallel Processing and Applied Mathematics

12th International Conference, PPAM 2017, Lublin, Poland, September 10-13, 2017, Revised Selected Papers

Author: Roman Wyrzykowski,Jack Dongarra,Ewa Deelman,Konrad Karczewski

Publisher: Springer

ISBN: 3319780549

Category: Computers

Page: 488

View: 4791

The two-volume set LNCS 10777 and 10778 constitutes revised selected papers from the 12th International Conference on Parallel Processing and Applied Mathematics, PPAM 2017, held in Lublin, Poland, in September 2017. The 49 regular papers presented in the proceedings were selected from 98 submissions. For the workshops and special sessions, that were held as integral parts of the PPAM 2017 conference, a total of 51 papers was accepted from 75 submissions. The papers were organized in topical sections named as follows: Part I: numerical algorithms and parallel scientific computing; particle methods in simulations; task-based paradigm of parallel computing; GPU computing; parallel non-numerical algorithms; performance evaluation of parallel algorithms and applications; environments and frameworks for parallel/distributed/cloud computing; applications of parallel computing; soft computing with applications; and special session on parallel matrix factorizations. Part II: workshop on models, algorithms and methodologies for hybrid parallelism in new HPC systems; workshop power and energy aspects of computations (PEAC 2017); workshop on scheduling for parallel computing (SPC 2017); workshop on language-based parallel programming models (WLPP 2017); workshop on PGAS programming; minisymposium on HPC applications in physical sciences; minisymposium on high performance computing interval methods; workshop on complex collective systems.

High Performance Computing

Second Latin American Conference, CARLA 2015, Petrópolis, Brazil, August 26-28, 2015, Proceedings

Author: Carla Osthoff,Philippe Olivier Alexandre Navaux,Carlos Jaime Barrios Hernandez,Pedro L. Silva Dias

Publisher: Springer

ISBN: 3319269283

Category: Computers

Page: 151

View: 1569

This book constitutes the proceedings of the Second Latin American Conference on High Performance Computing, CARLA 2015, a joint conference of the High-Performance Computing Latin America Community, HPCLATAM, and the Conferencia Latino Americana de Computación de Alto Rendimiento, CLCAR, held in Petrópolis, Brazil, in August 2015. The 11 papers presented in this volume were carefully reviewed and selected from 17 submissions. They were organized in topical sections named: grid and cloud computing; GPU & MIC Computing: methods, libraries and applications; and scientific computing applications.

Numerical Solution of Partial Differential Equations by the Finite Element Method

Author: Claes Johnson

Publisher: Courier Corporation

ISBN: 0486131599

Category: Mathematics

Page: 288

View: 6877

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.

A First Course in the Numerical Analysis of Differential Equations

Author: A. Iserles

Publisher: Cambridge University Press

ISBN: 0521734908

Category: Mathematics

Page: 459

View: 470

lead the reader to a theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations." --Book Jacket.

Spectral Methods in MATLAB

Author: Lloyd N. Trefethen

Publisher: SIAM

ISBN: 0898714656

Category: Mathematics

Page: 165

View: 6732

Mathematics of Computing -- Numerical Analysis.

Advanced Mathematical Methods for Scientists and Engineers I

Asymptotic Methods and Perturbation Theory

Author: Carl M. Bender,Steven A. Orszag

Publisher: Springer Science & Business Media

ISBN: 1475730691

Category: Mathematics

Page: 593

View: 549

A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.

Numerical Solution of Differential Equations

Author: Zhilin Li,Zhonghua Qiao,Tao Tang

Publisher: Cambridge University Press

ISBN: 1107163226

Category: Mathematics

Page: 293

View: 9964

A practical and concise guide to finite difference and finite element methods. Well-tested MATLAB® codes are available online.

Ten Lectures on Wavelets

Author: Ingrid Daubechies

Publisher: SIAM

ISBN: 9781611970104

Category: Wavelets (Mathematics)

Page: 357

View: 5045

Wavelets are a mathematical development that may revolutionize the world of information storage and retrieval according to many experts. They are a fairly simple mathematical tool now being applied to the compression of data--such as fingerprints, weather satellite photographs, and medical x-rays--that were previously thought to be impossible to condense without losing crucial details. This monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMS-NSF Conference on Wavelets and Applications. The author has worked on several aspects of the wavelet transform and has developed a collection of wavelets that are remarkably efficient.

Finite Difference Computing with PDEs

A Modern Software Approach

Author: Hans Petter Langtangen,Svein Linge

Publisher: Springer

ISBN: 3319554565

Category: Computers

Page: 507

View: 5197

This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

Applied Asymptotic Analysis

Author: Peter David Miller

Publisher: American Mathematical Soc.

ISBN: 0821840789

Category: Mathematics

Page: 467

View: 5521

"The book is intended for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and applied mathematics as well as science and engineering. The basic prerequisite is a background in differential equations, linear algebra, advanced calculus, and complex variables at the level of introductory undergraduate courses on these subjects."--BOOK JACKET.

The Mathematics of Diffusion

Author: John Crank

Publisher: Oxford University Press

ISBN: 9780198534112

Category: Mathematics

Page: 414

View: 8399

Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.

Practical Applied Mathematics

Modelling, Analysis, Approximation

Author: Sam Howison

Publisher: Cambridge University Press

ISBN: 9780521842747

Category: Mathematics

Page: 326

View: 982

Drawing from a wide variety of mathematical subjects, this book aims to show how mathematics is realised in practice in the everyday world. Dozens of applications are used to show that applied mathematics is much more than a series of academic calculations. Mathematical topics covered include distributions, ordinary and partial differential equations, and asymptotic methods as well as basics of modelling. The range of applications is similarly varied, from the modelling of hair to piano tuning, egg incubation and traffic flow. The style is informal but not superficial. In addition, the text is supplemented by a large number of exercises and sideline discussions, assisting the reader's grasp of the material. Used either in the classroom by upper-undergraduate students, or as extra reading for any applied mathematician, this book illustrates how the reader's knowledge can be used to describe the world around them.

Computational Methods for Astrophysical Fluid Flow

Saas-Fee Advanced Course 27. Lecture Notes 1997 Swiss Society for Astrophysics and Astronomy

Author: Randall J. LeVeque,Dimitri Mihalas,E.A. Dorfi,Ewald Müller

Publisher: Springer Science & Business Media

ISBN: 3540316329

Category: Science

Page: 510

View: 5203

This book leads directly to the most modern numerical techniques for compressible fluid flow, with special consideration given to astrophysical applications. Emphasis is put on high-resolution shock-capturing finite-volume schemes based on Riemann solvers. The applications of such schemes, in particular the PPM method, are given and include large-scale simulations of supernova explosions by core collapse and thermonuclear burning and astrophysical jets. Parts two and three treat radiation hydrodynamics. The power of adaptive (moving) grids is demonstrated with a number of stellar-physical simulations showing very crispy shock-front structures.

Mathematical Models in Biology

Author: Leah Edelstein-Keshet

Publisher: SIAM

ISBN: 9780898719147

Category: Biology

Page: 586

View: 1191

Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.