Spline Collocation Methods For Partial Differential Equations

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Spline Collocation Methods for Partial Differential Equations

William E. Schiesser
Spline Collocation Methods for Partial Differential Equations Book PDF

Author : William E. Schiesser
Publisher : John Wiley & Sons
Page : 576 pages
File Size : 41,6 Mb
Release : 2017-04-24
Category : Mathematics
ISBN : 9781119301059

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Spline Collocation Methods for Partial Differential Equations by William E. Schiesser Pdf

A comprehensive approach to numerical partial differential equations Spline Collocation Methods for Partial Differential Equations combines the collocation analysis of partial differential equations (PDEs) with the method of lines (MOL) in order to simplify the solution process. Using a series of example applications, the author delineates the main features of the approach in detail, including an established mathematical framework. The book also clearly demonstrates that spline collocation can offer a comprehensive method for numerical integration of PDEs when it is used with the MOL in which spatial (boundary value) derivatives are approximated with splines, including the boundary conditions. R, an open-source scientific programming system, is used throughout for programming the PDEs and numerical algorithms, and each section of code is clearly explained. As a result, readers gain a complete picture of the model and its computer implementation without having to fill in the details of the numerical analysis, algorithms, or programming. The presentation is not heavily mathematical, and in place of theorems and proofs, detailed example applications are provided. Appropriate for scientists, engineers, and applied mathematicians, Spline Collocation Methods for Partial Differential Equations: Introduces numerical methods by first presenting basic examples followed by more complicated applications Employs R to illustrate accurate and efficient solutions of the PDE models Presents spline collocation as a comprehensive approach to the numerical integration of PDEs and an effective alternative to other, well established methods Discusses how to reproduce and extend the presented numerical solutions Identifies the use of selected algorithms, such as the solution of nonlinear equations and banded or sparse matrix processing Features a companion website that provides the related R routines Spline Collocation Methods for Partial Differential Equations is a valuable reference and/or self-study guide for academics, researchers, and practitioners in applied mathematics and engineering, as well as for advanced undergraduates and graduate-level students.

Partial Differential Equations

D. Sloan,S. Vandewalle,E. Süli
Partial Differential Equations Book PDF

Author : D. Sloan,S. Vandewalle,E. Süli
Publisher : Elsevier
Page : 480 pages
File Size : 55,7 Mb
Release : 2012-12-02
Category : Mathematics
ISBN : 9780080929569

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Partial Differential Equations by D. Sloan,S. Vandewalle,E. Süli Pdf

/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight into the underlying stability and accuracy properties of computational algorithms for PDEs was deepened by building upon recent progress in mathematical analysis and in the theory of PDEs. To embark on a comprehensive review of the field of numerical analysis of partial differential equations within a single volume of this journal would have been an impossible task. Indeed, the 16 contributions included here, by some of the foremost world authorities in the subject, represent only a small sample of the major developments. We hope that these articles will, nevertheless, provide the reader with a stimulating glimpse into this diverse, exciting and important field. The opening paper by Thomée reviews the history of numerical analysis of PDEs, starting with the 1928 paper by Courant, Friedrichs and Lewy on the solution of problems of mathematical physics by means of finite differences. This excellent survey takes the reader through the development of finite differences for elliptic problems from the 1930s, and the intense study of finite differences for general initial value problems during the 1950s and 1960s. The formulation of the concept of stability is explored in the Lax equivalence theorem and the Kreiss matrix lemmas. Reference is made to the introduction of the finite element method by structural engineers, and a description is given of the subsequent development and mathematical analysis of the finite element method with piecewise polynomial approximating functions. The penultimate section of Thomée's survey deals with `other classes of approximation methods', and this covers methods such as collocation methods, spectral methods, finite volume methods and boundary integral methods. The final section is devoted to numerical linear algebra for elliptic problems. The next three papers, by Bialecki and Fairweather, Hesthaven and Gottlieb and Dahmen, describe, respectively, spline collocation methods, spectral methods and wavelet methods. The work by Bialecki and Fairweather is a comprehensive overview of orthogonal spline collocation from its first appearance to the latest mathematical developments and applications. The emphasis throughout is on problems in two space dimensions. The paper by Hesthaven and Gottlieb presents a review of Fourier and Chebyshev pseudospectral methods for the solution of hyperbolic PDEs. Particular emphasis is placed on the treatment of boundaries, stability of time discretisations, treatment of non-smooth solutions and multidomain techniques. The paper gives a clear view of the advances that have been made over the last decade in solving hyperbolic problems by means of spectral methods, but it shows that many critical issues remain open. The paper by Dahmen reviews the recent rapid growth in the use of wavelet methods for PDEs. The author focuses on the use of adaptivity, where significant successes have recently been achieved. He describes the potential weaknesses of wavelet methods as well as the perceived strengths, thus giving a balanced view that should encourage the study of wavelet methods.

Advance Numerical Techniques to Solve Linear and Nonlinear Differential Equations

Geeta Arora,Mangey Ram
Advance Numerical Techniques to Solve Linear and Nonlinear Differential Equations Book PDF

Author : Geeta Arora,Mangey Ram
Publisher : CRC Press
Page : 177 pages
File Size : 48,9 Mb
Release : 2024-01-23
Category : Mathematics
ISBN : 9781003811022

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Advance Numerical Techniques to Solve Linear and Nonlinear Differential Equations by Geeta Arora,Mangey Ram Pdf

Real-world issues can be translated into the language and concepts of mathematics with the use of mathematical models. Models guided by differential equations with intuitive solutions can be used throughout engineering and the sciences. Almost any changing system may be described by a set of differential equations. They may be found just about anywhere you look in fields including physics, engineering, economics, sociology, biology, business, healthcare, etc. The nature of these equations has been investigated by several mathematicians over the course of hundreds of years and, consequently, numerous effective methods for solving them have been created. It is often impractical to find a purely analytical solution to a system described by a differential equation because either the system itself is too complex or the system being described is too vast. Numerical approaches and computer simulations are especially helpful in such systems. The content provided in this book involves real-world examples, explores research challenges in numerical treatment, and demonstrates how to create new numerical methods for resolving problems. Theories and practical applications in the sciences and engineering are also discussed. Students of engineering and applied mathematics, as well as researchers and engineers who use computers to solve problems numerically or oversee those who do, will find this book focusing on advance numerical techniques to solve linear and nonlinear differential equations useful.

Splines and Variational Methods

P. M. Prenter
Splines and Variational Methods Book PDF

Author : P. M. Prenter
Publisher : Courier Corporation
Page : 338 pages
File Size : 46,5 Mb
Release : 2013-11-26
Category : Mathematics
ISBN : 9780486783499

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Splines and Variational Methods by P. M. Prenter Pdf

One of the clearest available introductions to variational methods, this text requires only a minimal background in calculus and linear algebra. Its self-contained treatment explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. The text’s first half concerns approximation theoretic notions, exploring the theory and computation of one- and two-dimensional polynomial and other spline functions. Later chapters examine variational methods in the solution of operator equations, focusing on boundary value problems in one and two dimensions. Additional topics include least squares and other Galerkin methods. Many helpful definitions, examples, and exercises appear throughout the book. A classic reference in spline theory, this volume will benefit experts as well as students of engineering and mathematics.

Mathematics for Large Scale Computing

Julio Diaz
Mathematics for Large Scale Computing Book PDF

Author : Julio Diaz
Publisher : CRC Press
Page : 362 pages
File Size : 45,6 Mb
Release : 2020-06-29
Category : Mathematics
ISBN : 9781000657630

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Mathematics for Large Scale Computing by Julio Diaz Pdf

During recent years a great deal of interest has been devoted to large scale computing applications. This has occurred in great part because of the introduction of advanced high performance computer architectures. The book contains survey articles as well as chapters on specific research applications, development and analysis of numerical algorithms, and performance evaluation of algorithms on advanced architectures. The effect of specialized architectural features on the performance of large scale computation is also considered by several authors. Several areas of applications are represented, including the numerical solution of partial differential equations, iterative techniques for large structured problems, the numerical solution of boundary value problems for ordinary differential equations, numerical optimization, and numerical quadrature. Mathematical issues in computer architecture are also presented, including the description of grey codes for generalized hypercubes. The results presented in this volume give, in our opinion, a representative picture of today’s state of the art in several aspects of large scale computing.

Advanced Mathematical Techniques in Engineering Sciences

Mangey Ram,J. Paulo Davim
Advanced Mathematical Techniques in Engineering Sciences Book PDF

Author : Mangey Ram,J. Paulo Davim
Publisher : CRC Press
Page : 334 pages
File Size : 41,7 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351371889

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Advanced Mathematical Techniques in Engineering Sciences by Mangey Ram,J. Paulo Davim Pdf

The goal of this book is to publish the latest mathematical techniques, research, and developments in engineering. This book includes a comprehensive range of mathematics applied in engineering areas for different tasks. Various mathematical tools, techniques, strategies, and methods in engineering applications are covered in each chapter. Mathematical techniques are the strength of engineering sciences and form the common foundation of all novel disciplines within the field. Advanced Mathematical Techniques in Engineering Sciences provides an ample range of mathematical tools and techniques applied across various fields of engineering sciences. Using this book, engineers will gain a greater understanding of the practical applications of mathematics in engineering sciences. Features Covers the mathematical techniques applied in engineering sciences Focuses on the latest research in the field of engineering applications Provides insights on an international and transnational scale Offers new studies and research in modeling and simulation

Nonlinear Partial Differential Equations in Engineering

W. F. Ames
Nonlinear Partial Differential Equations in Engineering Book PDF

Author : W. F. Ames
Publisher : Academic Press
Page : 528 pages
File Size : 46,9 Mb
Release : 1965-01-01
Category : Mathematics
ISBN : 9780080955247

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Nonlinear Partial Differential Equations in Engineering by W. F. Ames Pdf

Nonlinear Partial Differential Equations in Engineering

Advances in Computer Methods for Partial Differential Equations-VI

Robert Vichnevetsky,Robert S. Stepleman
Advances in Computer Methods for Partial Differential Equations VI Book PDF

Author : Robert Vichnevetsky,Robert S. Stepleman
Publisher : Unknown
Page : 588 pages
File Size : 41,8 Mb
Release : 1987
Category : Differential equations, Partial
ISBN : UOM:39015019485989

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Advances in Computer Methods for Partial Differential Equations-VI by Robert Vichnevetsky,Robert S. Stepleman Pdf

Intelligent Mathematical Software Systems

E.N. Houstis,R. Vichnevetsky,J.R. Rice
Intelligent Mathematical Software Systems Book PDF

Author : E.N. Houstis,R. Vichnevetsky,J.R. Rice
Publisher : Elsevier
Page : 378 pages
File Size : 52,7 Mb
Release : 1990-07-03
Category : Computers
ISBN : 9780444599230

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Intelligent Mathematical Software Systems by E.N. Houstis,R. Vichnevetsky,J.R. Rice Pdf

Most of the well-known mathematical software systems are batch oriented, though in the past few years there have been attempts to incorporate ``knowledge'' or ``expertise'' into these systems. A number of developments have helped in making the systems more powerful and user-friendly: algorithm/parameter selection for the solution of well-defined mathematical engineering problems; parallel computing; computer graphics technology; interface development tools; and of course the years of experience with these systems and the increase in available computing power have made it practical to fulfill the potential seen in the early years of their development. This book covers four main areas of the subject: Application Oriented Expert Systems, Advisory Systems, Knowledge Manipulation Issues, and User Interfaces.

Recent Trends in Physics of Material Science and Technology

Ford Lumban Gaol,Keshav Shrivastava,Jamil Akhtar
Recent Trends in Physics of Material Science and Technology Book PDF

Author : Ford Lumban Gaol,Keshav Shrivastava,Jamil Akhtar
Publisher : Springer
Page : 353 pages
File Size : 45,7 Mb
Release : 2014-12-27
Category : Science
ISBN : 9789812871282

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Recent Trends in Physics of Material Science and Technology by Ford Lumban Gaol,Keshav Shrivastava,Jamil Akhtar Pdf

This book discusses in detail the recent trends in Computational Physics, Nano-physics and Devices Technology. Numerous modern devices with very high accuracy, are explored In conditions such as longevity and extended possibilities to work in wide temperature and pressure ranges, aggressive media, etc. This edited volume presents 32 selected papers of the 2013 International Conference on Science & Engineering in Mathematics, Chemistry and Physics. The book is divided into three scientific Sections: (i) Computational Physics, (ii) Nanophysics and Technology, (iii) Devices and Systems and is addressed to Professors, post-graduate students, scientists and engineers taking part in R&D of nano-materials, ferro-piezoelectrics, computational Physics and devices system, and also different devices based on broad applications in different areas of modern science and technology.

Advances in Computer Methods for Partial Differential Equations-V

Robert Vichnevetsky,Robert S. Stepleman
Advances in Computer Methods for Partial Differential Equations V Book PDF

Author : Robert Vichnevetsky,Robert S. Stepleman
Publisher : Unknown
Page : 580 pages
File Size : 42,8 Mb
Release : 1984
Category : Differential equations, Partial
ISBN : UOM:39015015704813

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Advances in Computer Methods for Partial Differential Equations-V by Robert Vichnevetsky,Robert S. Stepleman Pdf