An Introductory Guide to Computational Methods for the Solution of Physics Problems

An Introductory Guide to Computational Methods for the Solution of Physics Problems

Author: George Rawitscher

Publisher:

Published: 2018

Total Pages: 221

ISBN-13: 9783319427041

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This monograph presents fundamental aspects of modern spectral and other computational methods, which are not generally taught in traditional courses. It emphasizes concepts as errors, convergence, stability, order and efficiency applied to the solution of physical problems. The spectral methods consist in expanding the function to be calculated into a set of appropriate basis functions (generally orthogonal polynomials) and the respective expansion coefficients are obtained via collocation equations. The main advantage of these methods is that they simultaneously take into account all available information, rather only the information available at a limited number of mesh points. They require more complicated matrix equations than those obtained in finite difference methods. However, the elegance, speed, and accuracy of the spectral methods more than compensates for any such drawbacks. During the course of the monograph, the authors examine the usually rapid convergence of the spectral expansions and the improved accuracy that results when nonequispaced support points are used, in contrast to the equispaced points used in finite difference methods. In particular, they demonstrate the enhanced accuracy obtained in the solution of integral equations. The monograph includes an informative introduction to old and new computational methods with numerous practical examples, while at the same time pointing out the errors that each of the available algorithms introduces into the specific solution. It is a valuable resource for undergraduate students as an introduction to the field and for graduate students wishing to compare the available computational methods. In addition, the work develops the criteria required for students to select the most suitable method to solve the particular scientific problem that they are confronting.


Book Synopsis An Introductory Guide to Computational Methods for the Solution of Physics Problems by : George Rawitscher

Download or read book An Introductory Guide to Computational Methods for the Solution of Physics Problems written by George Rawitscher and published by . This book was released on 2018 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents fundamental aspects of modern spectral and other computational methods, which are not generally taught in traditional courses. It emphasizes concepts as errors, convergence, stability, order and efficiency applied to the solution of physical problems. The spectral methods consist in expanding the function to be calculated into a set of appropriate basis functions (generally orthogonal polynomials) and the respective expansion coefficients are obtained via collocation equations. The main advantage of these methods is that they simultaneously take into account all available information, rather only the information available at a limited number of mesh points. They require more complicated matrix equations than those obtained in finite difference methods. However, the elegance, speed, and accuracy of the spectral methods more than compensates for any such drawbacks. During the course of the monograph, the authors examine the usually rapid convergence of the spectral expansions and the improved accuracy that results when nonequispaced support points are used, in contrast to the equispaced points used in finite difference methods. In particular, they demonstrate the enhanced accuracy obtained in the solution of integral equations. The monograph includes an informative introduction to old and new computational methods with numerous practical examples, while at the same time pointing out the errors that each of the available algorithms introduces into the specific solution. It is a valuable resource for undergraduate students as an introduction to the field and for graduate students wishing to compare the available computational methods. In addition, the work develops the criteria required for students to select the most suitable method to solve the particular scientific problem that they are confronting.

An Introductory Guide to Computational Methods for the Solution of Physics Problems

An Introductory Guide to Computational Methods for the Solution of Physics Problems

Author: George Rawitscher

Publisher: Springer

Published: 2018-10-24

Total Pages: 221

ISBN-13: 3319427032

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This monograph presents fundamental aspects of modern spectral and other computational methods, which are not generally taught in traditional courses. It emphasizes concepts as errors, convergence, stability, order and efficiency applied to the solution of physical problems. The spectral methods consist in expanding the function to be calculated into a set of appropriate basis functions (generally orthogonal polynomials) and the respective expansion coefficients are obtained via collocation equations. The main advantage of these methods is that they simultaneously take into account all available information, rather only the information available at a limited number of mesh points. They require more complicated matrix equations than those obtained in finite difference methods. However, the elegance, speed, and accuracy of the spectral methods more than compensates for any such drawbacks. During the course of the monograph, the authors examine the usually rapid convergence of the spectral expansions and the improved accuracy that results when nonequispaced support points are used, in contrast to the equispaced points used in finite difference methods. In particular, they demonstrate the enhanced accuracy obtained in the solutionof integral equations. The monograph includes an informative introduction to old and new computational methods with numerous practical examples, while at the same time pointing out the errors that each of the available algorithms introduces into the specific solution. It is a valuable resource for undergraduate students as an introduction to the field and for graduate students wishing to compare the available computational methods. In addition, the work develops the criteria required for students to select the most suitable method to solve the particular scientific problem that they are confronting.


Book Synopsis An Introductory Guide to Computational Methods for the Solution of Physics Problems by : George Rawitscher

Download or read book An Introductory Guide to Computational Methods for the Solution of Physics Problems written by George Rawitscher and published by Springer. This book was released on 2018-10-24 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents fundamental aspects of modern spectral and other computational methods, which are not generally taught in traditional courses. It emphasizes concepts as errors, convergence, stability, order and efficiency applied to the solution of physical problems. The spectral methods consist in expanding the function to be calculated into a set of appropriate basis functions (generally orthogonal polynomials) and the respective expansion coefficients are obtained via collocation equations. The main advantage of these methods is that they simultaneously take into account all available information, rather only the information available at a limited number of mesh points. They require more complicated matrix equations than those obtained in finite difference methods. However, the elegance, speed, and accuracy of the spectral methods more than compensates for any such drawbacks. During the course of the monograph, the authors examine the usually rapid convergence of the spectral expansions and the improved accuracy that results when nonequispaced support points are used, in contrast to the equispaced points used in finite difference methods. In particular, they demonstrate the enhanced accuracy obtained in the solutionof integral equations. The monograph includes an informative introduction to old and new computational methods with numerous practical examples, while at the same time pointing out the errors that each of the available algorithms introduces into the specific solution. It is a valuable resource for undergraduate students as an introduction to the field and for graduate students wishing to compare the available computational methods. In addition, the work develops the criteria required for students to select the most suitable method to solve the particular scientific problem that they are confronting.

Computational Problems for Physics

Computational Problems for Physics

Author: Rubin H. Landau

Publisher: CRC Press

Published: 2018-05-30

Total Pages: 465

ISBN-13: 1351784021

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Our future scientists and professionals must be conversant in computational techniques. In order to facilitate integration of computer methods into existing physics courses, this textbook offers a large number of worked examples and problems with fully guided solutions in Python as well as other languages (Mathematica, Java, C, Fortran, and Maple). It’s also intended as a self-study guide for learning how to use computer methods in physics. The authors include an introductory chapter on numerical tools and indication of computational and physics difficulty level for each problem. Readers also benefit from the following features: • Detailed explanations and solutions in various coding languages. • Problems are ranked based on computational and physics difficulty. • Basics of numerical methods covered in an introductory chapter. • Programming guidance via flowcharts and pseudocode. Rubin Landau is a Distinguished Professor Emeritus in the Department of Physics at Oregon State University in Corvallis and a Fellow of the American Physical Society (Division of Computational Physics). Manuel Jose Paez-Mejia is a Professor of Physics at Universidad de Antioquia in Medellín, Colombia.


Book Synopsis Computational Problems for Physics by : Rubin H. Landau

Download or read book Computational Problems for Physics written by Rubin H. Landau and published by CRC Press. This book was released on 2018-05-30 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our future scientists and professionals must be conversant in computational techniques. In order to facilitate integration of computer methods into existing physics courses, this textbook offers a large number of worked examples and problems with fully guided solutions in Python as well as other languages (Mathematica, Java, C, Fortran, and Maple). It’s also intended as a self-study guide for learning how to use computer methods in physics. The authors include an introductory chapter on numerical tools and indication of computational and physics difficulty level for each problem. Readers also benefit from the following features: • Detailed explanations and solutions in various coding languages. • Problems are ranked based on computational and physics difficulty. • Basics of numerical methods covered in an introductory chapter. • Programming guidance via flowcharts and pseudocode. Rubin Landau is a Distinguished Professor Emeritus in the Department of Physics at Oregon State University in Corvallis and a Fellow of the American Physical Society (Division of Computational Physics). Manuel Jose Paez-Mejia is a Professor of Physics at Universidad de Antioquia in Medellín, Colombia.

Computational Methods for Physics

Computational Methods for Physics

Author: Joel Franklin

Publisher: Cambridge University Press

Published: 2013-05-23

Total Pages: 419

ISBN-13: 1107067855

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There is an increasing need for undergraduate students in physics to have a core set of computational tools. Most problems in physics benefit from numerical methods, and many of them resist analytical solution altogether. This textbook presents numerical techniques for solving familiar physical problems where a complete solution is inaccessible using traditional mathematical methods. The numerical techniques for solving the problems are clearly laid out, with a focus on the logic and applicability of the method. The same problems are revisited multiple times using different numerical techniques, so readers can easily compare the methods. The book features over 250 end-of-chapter exercises. A website hosted by the author features a complete set of programs used to generate the examples and figures, which can be used as a starting point for further investigation. A link to this can be found at www.cambridge.org/9781107034303.


Book Synopsis Computational Methods for Physics by : Joel Franklin

Download or read book Computational Methods for Physics written by Joel Franklin and published by Cambridge University Press. This book was released on 2013-05-23 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is an increasing need for undergraduate students in physics to have a core set of computational tools. Most problems in physics benefit from numerical methods, and many of them resist analytical solution altogether. This textbook presents numerical techniques for solving familiar physical problems where a complete solution is inaccessible using traditional mathematical methods. The numerical techniques for solving the problems are clearly laid out, with a focus on the logic and applicability of the method. The same problems are revisited multiple times using different numerical techniques, so readers can easily compare the methods. The book features over 250 end-of-chapter exercises. A website hosted by the author features a complete set of programs used to generate the examples and figures, which can be used as a starting point for further investigation. A link to this can be found at www.cambridge.org/9781107034303.

Computational Physics

Computational Physics

Author: Rubin H. Landau

Publisher: Wiley-VCH

Published: 1997-08-11

Total Pages: 564

ISBN-13:

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Help students master real-world problems as they develop new insight into the physical sciences Problems in the physical sciences that once baffled and frustrated scientists can now be solved easily with the aid of a computer. Computers can quickly complete complex calculations, provide numerical simulations of natural systems, and explore the unknown. Computational Physics shows students how to use computers to solve scientific problems and understand systems at a level previously possible only in a research environment. Adaptable to a ten-week class or a full-year course, it provides C and Fortran programs that can be modified and rewritten as needed to implement a wide range of computational projects. Light on theory, heavy on applications, this practical, easy-to-understand guide * Presents material from a problem-oriented perspective * Integrates physics, computer science, and numerical methods and statistics * Encourages creative thinking and an object-oriented view of problem solving * Provides C and Fortran programs for implementing most of the projects * Provides samples of problems actually solved in two ten-week quarters * Includes a 3.5'' floppy disk containing the codes featured in the text * Offers multimedia demonstrations and updates on a complementary Web site With this engaging book as a guide, advanced undergraduates and first-year graduate students will gain confidence in their abilities and develop new insight into the physical sciences as they use their computers to address challenging and stimulating problems.


Book Synopsis Computational Physics by : Rubin H. Landau

Download or read book Computational Physics written by Rubin H. Landau and published by Wiley-VCH. This book was released on 1997-08-11 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: Help students master real-world problems as they develop new insight into the physical sciences Problems in the physical sciences that once baffled and frustrated scientists can now be solved easily with the aid of a computer. Computers can quickly complete complex calculations, provide numerical simulations of natural systems, and explore the unknown. Computational Physics shows students how to use computers to solve scientific problems and understand systems at a level previously possible only in a research environment. Adaptable to a ten-week class or a full-year course, it provides C and Fortran programs that can be modified and rewritten as needed to implement a wide range of computational projects. Light on theory, heavy on applications, this practical, easy-to-understand guide * Presents material from a problem-oriented perspective * Integrates physics, computer science, and numerical methods and statistics * Encourages creative thinking and an object-oriented view of problem solving * Provides C and Fortran programs for implementing most of the projects * Provides samples of problems actually solved in two ten-week quarters * Includes a 3.5'' floppy disk containing the codes featured in the text * Offers multimedia demonstrations and updates on a complementary Web site With this engaging book as a guide, advanced undergraduates and first-year graduate students will gain confidence in their abilities and develop new insight into the physical sciences as they use their computers to address challenging and stimulating problems.

Computational Methods in Physics, Chemistry and Biology

Computational Methods in Physics, Chemistry and Biology

Author: Paul Harrison

Publisher: John Wiley & Sons

Published: 2001-11-28

Total Pages: 230

ISBN-13: 9780471495635

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Eine gut verständliche Einführung in moderne naturwissenschaftliche Rechenmethoden! Nur geringe physikalische Vorkenntnisse voraussetzend, vermittelt der Autor Grundlagen und komplexere Ansätze anhand vieler Beispiele und ausgesprochen praxisnaher Übungsaufgaben. Besprochen werden alle Rechenmethoden, die im Grundstudium erlernt werden sollen, hinsichtlich ihrer Leistungsfähigkeit und ihrer Anwendungsgebiete.


Book Synopsis Computational Methods in Physics, Chemistry and Biology by : Paul Harrison

Download or read book Computational Methods in Physics, Chemistry and Biology written by Paul Harrison and published by John Wiley & Sons. This book was released on 2001-11-28 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eine gut verständliche Einführung in moderne naturwissenschaftliche Rechenmethoden! Nur geringe physikalische Vorkenntnisse voraussetzend, vermittelt der Autor Grundlagen und komplexere Ansätze anhand vieler Beispiele und ausgesprochen praxisnaher Übungsaufgaben. Besprochen werden alle Rechenmethoden, die im Grundstudium erlernt werden sollen, hinsichtlich ihrer Leistungsfähigkeit und ihrer Anwendungsgebiete.

Computational Methods in Physics

Computational Methods in Physics

Author: Simon Širca

Publisher: Springer

Published: 2018-06-21

Total Pages: 880

ISBN-13: 3319786199

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This book is intended to help advanced undergraduate, graduate, and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues, as well as optimization of program execution speeds. Numerous examples are given throughout the chapters, followed by comprehensive end-of-chapter problems with a more pronounced physics background, while less stress is given to the explanation of individual algorithms. The readers are encouraged to develop a certain amount of skepticism and scrutiny instead of blindly following readily available commercial tools. The second edition has been enriched by a chapter on inverse problems dealing with the solution of integral equations, inverse Sturm-Liouville problems, as well as retrospective and recovery problems for partial differential equations. The revised text now includes an introduction to sparse matrix methods, the solution of matrix equations, and pseudospectra of matrices; it discusses the sparse Fourier, non-uniform Fourier and discrete wavelet transformations, the basics of non-linear regression and the Kolmogorov-Smirnov test; it demonstrates the key concepts in solving stiff differential equations and the asymptotics of Sturm-Liouville eigenvalues and eigenfunctions. Among other updates, it also presents the techniques of state-space reconstruction, methods to calculate the matrix exponential, generate random permutations and compute stable derivatives.


Book Synopsis Computational Methods in Physics by : Simon Širca

Download or read book Computational Methods in Physics written by Simon Širca and published by Springer. This book was released on 2018-06-21 with total page 880 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to help advanced undergraduate, graduate, and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues, as well as optimization of program execution speeds. Numerous examples are given throughout the chapters, followed by comprehensive end-of-chapter problems with a more pronounced physics background, while less stress is given to the explanation of individual algorithms. The readers are encouraged to develop a certain amount of skepticism and scrutiny instead of blindly following readily available commercial tools. The second edition has been enriched by a chapter on inverse problems dealing with the solution of integral equations, inverse Sturm-Liouville problems, as well as retrospective and recovery problems for partial differential equations. The revised text now includes an introduction to sparse matrix methods, the solution of matrix equations, and pseudospectra of matrices; it discusses the sparse Fourier, non-uniform Fourier and discrete wavelet transformations, the basics of non-linear regression and the Kolmogorov-Smirnov test; it demonstrates the key concepts in solving stiff differential equations and the asymptotics of Sturm-Liouville eigenvalues and eigenfunctions. Among other updates, it also presents the techniques of state-space reconstruction, methods to calculate the matrix exponential, generate random permutations and compute stable derivatives.

Computational Physics

Computational Physics

Author: Franz J. Vesely

Publisher: Springer Science & Business Media

Published: 2013-04-18

Total Pages: 277

ISBN-13: 1475723075

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Author Franz J. Vesely offers students an introductory text on computational physics, providing them with the important basic numerical/computational techniques. His unique text sets itself apart from others by focusing on specific problems of computational physics. The author also provides a selection of modern fields of research. Students will benefit from the appendixes which offer a short description of some properties of computing and machines and outline the technique of 'Fast Fourier Transformation.'


Book Synopsis Computational Physics by : Franz J. Vesely

Download or read book Computational Physics written by Franz J. Vesely and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Author Franz J. Vesely offers students an introductory text on computational physics, providing them with the important basic numerical/computational techniques. His unique text sets itself apart from others by focusing on specific problems of computational physics. The author also provides a selection of modern fields of research. Students will benefit from the appendixes which offer a short description of some properties of computing and machines and outline the technique of 'Fast Fourier Transformation.'

Computational Techniques in Physics

Computational Techniques in Physics

Author: P. K. MacKeown

Publisher: Institute of Physics Publishing (GB)

Published: 1987

Total Pages: 248

ISBN-13:

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Book Synopsis Computational Techniques in Physics by : P. K. MacKeown

Download or read book Computational Techniques in Physics written by P. K. MacKeown and published by Institute of Physics Publishing (GB). This book was released on 1987 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computation in Modern Physics

Computation in Modern Physics

Author: William R Gibbs

Publisher: World Scientific Publishing Company

Published: 1999-11-22

Total Pages: 372

ISBN-13: 9813105569

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The use of computers to solve modern scientific problems is very widespread. The impact of the improvement of our techniques on the solution of complex problems is difficult to overstate. Even our approach to most problems has been changed. Solutions to problems once thought intractable are being routinely secured. Instead of using oversimplified models, as has been the practice for the treatment of scientific systems in the past, the entire problem can now be tackled successfully. The second edition of Computation in Modern Physics develops and presents algorithms for the solution of many types of mathematical systems, some dating as far as the last few centuries, but also quite a number that have been developed within the last 10–50 years. In this latter category, close attention is paid to the rapidly developing area of Monte Carlo techniques, where new conceptual views of physics problems are being brought into play. With this method, problems in a large number of dimensions can be solved through the introduction of a modern method for the representation of multidimensional functions. This invaluable book is suitable for two different levels of computational physics. The first part of the book is of an advanced introductory level and is appropriate for good students with no previous experience in computational methods or any student with some experience. Here the student is introduced to integral and differential techniques, Monte Carlo integration, basic computer architecture, methods of linear algebra, finite element techniques, digital signal processing and chaos. The second part of the book is more specialized for problems in strong interaction with emphasis on solutions to many-body scattering problems and several-body bound state calculations with Monte Carlo techniques. It also contains a chapter dealing with techniques for the summation of divergent series.


Book Synopsis Computation in Modern Physics by : William R Gibbs

Download or read book Computation in Modern Physics written by William R Gibbs and published by World Scientific Publishing Company. This book was released on 1999-11-22 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of computers to solve modern scientific problems is very widespread. The impact of the improvement of our techniques on the solution of complex problems is difficult to overstate. Even our approach to most problems has been changed. Solutions to problems once thought intractable are being routinely secured. Instead of using oversimplified models, as has been the practice for the treatment of scientific systems in the past, the entire problem can now be tackled successfully. The second edition of Computation in Modern Physics develops and presents algorithms for the solution of many types of mathematical systems, some dating as far as the last few centuries, but also quite a number that have been developed within the last 10–50 years. In this latter category, close attention is paid to the rapidly developing area of Monte Carlo techniques, where new conceptual views of physics problems are being brought into play. With this method, problems in a large number of dimensions can be solved through the introduction of a modern method for the representation of multidimensional functions. This invaluable book is suitable for two different levels of computational physics. The first part of the book is of an advanced introductory level and is appropriate for good students with no previous experience in computational methods or any student with some experience. Here the student is introduced to integral and differential techniques, Monte Carlo integration, basic computer architecture, methods of linear algebra, finite element techniques, digital signal processing and chaos. The second part of the book is more specialized for problems in strong interaction with emphasis on solutions to many-body scattering problems and several-body bound state calculations with Monte Carlo techniques. It also contains a chapter dealing with techniques for the summation of divergent series.