Numerical Methods for Initial Value Problems in Physics
This textbook is a comprehensive overview of the construction, implementation, and application of important numerical methods for the solution of Initial Value Problems (IVPs). Beginning with IVPs involving Ordinary Differential Equations (ODEs) and progressing to problems with Partial Differential...
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| פורמט: | אלקטרוני ספר אלקטרוני |
| שפה: | אנגלית |
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Cham :
Springer Nature Switzerland : Imprint: Springer,
2023.
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| מהדורה: | 1st ed. 2023. |
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| גישה מקוונת: | https://doi.org/10.1007/978-3-031-33556-3 |
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| 100 | 1 | |a Guzmán, Francisco S. |e author. |0 (orcid)0000-0002-1350-3673 |1 https://orcid.org/0000-0002-1350-3673 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Numerical Methods for Initial Value Problems in Physics |h [electronic resource] / |c by Francisco S. Guzmán. |
| 250 | |a 1st ed. 2023. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2023. | |
| 300 | |a 1 online resource (XIV, 357 p. 130 illus.). |b 9 illus. in color. | ||
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| 505 | 0 | |a Chapter1. Introduction -- Chapter2. Ordinary Differential Equations -- Chapter3. Simple Methods for Initial Value Problems Involving PDEs -- Chapter4. Method of Lines for Initial Value Problems Involving PDEs -- Chapter5. Finite Volume Methods -- Chapter6. Initial Value Problems in 3+1 and 2+1 dimensions -- Chapter7. Appendix A: Stability of Evolution Schemes -- Chapter8. Appendix B: Codes. | |
| 520 | |a This textbook is a comprehensive overview of the construction, implementation, and application of important numerical methods for the solution of Initial Value Problems (IVPs). Beginning with IVPs involving Ordinary Differential Equations (ODEs) and progressing to problems with Partial Differential Equations (PDEs) in 1+1 and 3+1 dimensions, it provides readers with a clear and systematic progression from simple to complex concepts. The numerical methods selected in this textbook can solve a considerable variety of problems and the applications presented cover a wide range of topics, including population dynamics, chaos, celestial mechanics, geophysics, astrophysics, and more. Each chapter contains a variety of solved problems and exercises, with code included. These examples are designed to motivate and inspire readers to delve deeper into the state-of-the-art problems in their own fields. The code is written in Fortran 90, in a library-free style, making them easy to program and efficient to run. The appendix also includes the same code in C++, making the book accessible to a variety of programming backgrounds. At the end of each chapter, there are brief descriptions of how the methods could be improved, along with one or two projects that can be developed with the methods and codes described. These projects are highly engaging, from synchronization of chaos and message encryption to gravitational waves emitted by a binary system and non-linear absorption of a scalar field. With its clear explanations, hands-on approach, and practical examples, this textbook is an essential resource for advanced undergraduate and graduate students who want to the learn how to use numerical methods to tackle challenging problems. | ||
| 532 | 8 | |a Accessibility summary: This PDF does Not fully comply with PDF/UA standards but does include limited screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility | |
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| 650 | 0 | |a Mathematical physics. | |
| 650 | 0 | |a Mathematics |x Data processing. | |
| 650 | 0 | |a Differential equations. | |
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| 650 | 2 | 4 | |a Computational Mathematics and Numerical Analysis. |
| 650 | 2 | 4 | |a Mathematical Physics. |
| 650 | 2 | 4 | |a Differential Equations. |
| 650 | 2 | 4 | |a Complex Systems. |
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