Finite Difference Methods for Ordinary and Partial Differential Equations

Steady-State and Time-Dependent Problems

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Author: Randall J. LeVeque

Publisher: SIAM

ISBN: 9780898717839

Category: Differential equations

Page: 339

View: 995

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

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Author: Randall J. LeVeque

Publisher: Cambridge University Press

ISBN: 1139434187

Category: Mathematics

Page: N.A

View: 1531

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.

Numerical Solution of Partial Differential Equations by the Finite Element Method

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Author: Claes Johnson

Publisher: Courier Corporation

ISBN: 0486131599

Category: Mathematics

Page: 288

View: 9176

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

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Author: A. Iserles

Publisher: Cambridge University Press

ISBN: 0521734908

Category: Mathematics

Page: 459

View: 4407

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.

High Performance Programming for Soft Computing

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Author: Oscar Humberto Montiel Ross,Roberto Sepulveda

Publisher: CRC Press

ISBN: 1466586028

Category: Computers

Page: 376

View: 1927

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

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Author: Anton Baranov,Sergei Kisliakov,Nikolai Nikolski

Publisher: Birkhäuser

ISBN: 3319590782

Category: Mathematics

Page: 484

View: 8441

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

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Author: Tobias Neckel,Florian Rupp

Publisher: Walter de Gruyter

ISBN: 8376560263

Category: Mathematics

Page: 650

View: 893

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

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

Publisher: Springer

ISBN: 3319780549

Category: Computers

Page: 488

View: 7696

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

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

Publisher: Springer

ISBN: 3319269283

Category: Computers

Page: 151

View: 3341

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.

Spectral Methods in MATLAB

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Author: Lloyd N. Trefethen

Publisher: SIAM

ISBN: 0898714656

Category: Mathematics

Page: 165

View: 9448

Mathematics of Computing -- Numerical Analysis.

Advanced Mathematical Methods for Scientists and Engineers I

Asymptotic Methods and Perturbation Theory

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Author: Carl M. Bender,Steven A. Orszag

Publisher: Springer Science & Business Media

ISBN: 1475730691

Category: Mathematics

Page: 593

View: 5956

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.

The Symmetric Eigenvalue Problem

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Author: Beresford N. Parlett

Publisher: SIAM

ISBN: 9781611971163

Category: Algebras, Linear

Page: 398

View: 1921

According to Parlett, "Vibrations are everywhere, and so too are the eigenvalues associated with them. As mathematical models invade more and more disciplines, we can anticipate a demand for eigenvalue calculations in an ever richer variety of contexts." Anyone who performs these calculations will welcome the reprinting of Parlett's book (originally published in 1980). In this unabridged, amended version, Parlett covers aspects of the problem that are not easily found elsewhere. The chapter titles convey the scope of the material succinctly. The aim of the book is to present mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few. The author explains why the selected information really matters and he is not shy about making judgments. The commentary is lively but the proofs are terse. The first nine chapters are based on a matrix on which it is possible to make similarity transformations explicitly. The only source of error is inexact arithmetic. The last five chapters turn to large sparse matrices and the task of making approximations and judging them.

Solving Least Squares Problems

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Author: Charles L. Lawson,Richard J. Hanson

Publisher: SIAM

ISBN: 0898713560

Category: Mathematics

Page: 337

View: 1309

This Classic edition includes a new appendix which summarizes the major developments since the book was originally published in 1974. The additions are organized in short sections associated with each chapter. An additional 230 references have been added, bringing the bibliography to over 400 entries. Appendix C has been edited to reflect changes in the associated software package and software distribution method.

Numerical Solution of Partial Differential Equations

An Introduction

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Author: K. W. Morton,D. F. Mayers

Publisher: Cambridge University Press

ISBN: 1139443208

Category: Mathematics

Page: N.A

View: 5089

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.

The Mathematics of Diffusion

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Author: John Crank

Publisher: Oxford University Press

ISBN: 9780198534112

Category: Mathematics

Page: 414

View: 5562

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.

Applied Asymptotic Analysis

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Author: Peter David Miller

Publisher: American Mathematical Soc.

ISBN: 0821840789

Category: Mathematics

Page: 467

View: 661

"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.

Finite Difference Methods in Financial Engineering

A Partial Differential Equation Approach

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Author: Daniel J. Duffy

Publisher: John Wiley & Sons

ISBN: 1118856481

Category: Business & Economics

Page: 464

View: 1425

The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method. In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature: Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options Early exercise features and approximation using front-fixing, penalty and variational methods Modelling stochastic volatility models using Splitting methods Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work Modelling jumps using Partial Integro Differential Equations (PIDE) Free and moving boundary value problems in QF Included with the book is a CD containing information on how to set up FDM algorithms, how to map these algorithms to C++ as well as several working programs for one-factor and two-factor models. We also provide source code so that you can customize the applications to suit your own needs.

A Multigrid Tutorial

Second Edition

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Author: William L. Briggs,Van Emden Henson,Steve F. McCormick

Publisher: SIAM

ISBN: 0898714621

Category: Mathematics

Page: 193

View: 5680

Mathematics of Computing -- Numerical Analysis.