Classical Numerical Methods in Scientific Computing
Partial differential equations are paramount in mathematical modelling with applications in engineering and science. The book starts with a crash course on partial differential equations in order to familiarize the reader with fundamental properties such as existence, uniqueness and possibly existin...
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| Main Authors: | , , |
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| Format: | Online |
| Language: | English |
| Published: |
TU Delft OPEN Publishing
2025
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| Online Access: | ONIX_20250522T133704_9789463667326_50 |
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| _version_ | 1869520146723241984 |
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| author | van Kan, Jos Segal, Guus Vermolen, Fred |
| author_browse | Segal, Guus Vermolen, Fred van Kan, Jos |
| author_facet | van Kan, Jos Segal, Guus Vermolen, Fred |
| author_sort | van Kan, Jos |
| collection | Directory of Open Access Books |
| description | Partial differential equations are paramount in mathematical modelling with applications in engineering and science. The book starts with a crash course on partial differential equations in order to familiarize the reader with fundamental properties such as existence, uniqueness and possibly existing maximum principles. The main topic of the book entails the description of classical numerical methods that are used to approximate the solution of partial differential equations. The focus is on discretization methods such as the finite difference, finite volume and finite element method. The manuscript also makes a short excursion to the solution of large sets of (non)linear algebraic equations that result after application of discretization method to partial differential equations. The book treats the construction of such discretization methods, as well as some error analysis, where it is noted that the error analysis for the finite element method is merely descriptive, rather than rigorous from a mathematical point of view. The last chapters focus on time integration issues for classical time-dependent partial differential equations. After reading the book, the reader should be able to derive finite element methods, to implement the methods and to judge whether the obtained approximations are consistent with the solution to the partial differential equations. The reader will also obtain these skills for the other classical discretization methods. Acquiring such fundamental knowledge will allow the reader to continue studying more advanced methods like meshfree methods, discontinuous Galerkin methods and spectral methods for the approximation of solutions to partial differential equations. |
| format | Online |
| id | doab-20.500.12854ir-160198 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | TU Delft OPEN Publishing |
| publisherStr | TU Delft OPEN Publishing |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1601982025-05-22T11:44:19Z Classical Numerical Methods in Scientific Computing van Kan, Jos Segal, Guus Vermolen, Fred partial differential equations finite element method discretization time integration mathematical modelling thema EDItEUR::P Mathematics and Science::PB Mathematics::PBC Mathematical foundations Partial differential equations are paramount in mathematical modelling with applications in engineering and science. The book starts with a crash course on partial differential equations in order to familiarize the reader with fundamental properties such as existence, uniqueness and possibly existing maximum principles. The main topic of the book entails the description of classical numerical methods that are used to approximate the solution of partial differential equations. The focus is on discretization methods such as the finite difference, finite volume and finite element method. The manuscript also makes a short excursion to the solution of large sets of (non)linear algebraic equations that result after application of discretization method to partial differential equations. The book treats the construction of such discretization methods, as well as some error analysis, where it is noted that the error analysis for the finite element method is merely descriptive, rather than rigorous from a mathematical point of view. The last chapters focus on time integration issues for classical time-dependent partial differential equations. After reading the book, the reader should be able to derive finite element methods, to implement the methods and to judge whether the obtained approximations are consistent with the solution to the partial differential equations. The reader will also obtain these skills for the other classical discretization methods. Acquiring such fundamental knowledge will allow the reader to continue studying more advanced methods like meshfree methods, discontinuous Galerkin methods and spectral methods for the approximation of solutions to partial differential equations. 2025-05-22T11:44:18Z 2025-05-22T11:44:18Z 2023 book ONIX_20250522T133704_9789463667326_50 9789463667326 https://directory.doabooks.org/handle/20.500.12854/160198 eng none image/png Attribution 4.0 International https://store.printservice.nl/ustorethemes/HR/150/nl-NL/products/4862/Classical-Numerical-Methods-in-Scientific-Computing/ https://books.open.tudelft.nl/home/catalog/view/168/293/542 TU Delft OPEN Publishing 10.59490/t.2023.007 10.59490/t.2023.007 6e038278-520e-4e74-a239-d06f0d179364 9789463667326 open access |
| spellingShingle | partial differential equations finite element method discretization time integration mathematical modelling thema EDItEUR::P Mathematics and Science::PB Mathematics::PBC Mathematical foundations van Kan, Jos Segal, Guus Vermolen, Fred Classical Numerical Methods in Scientific Computing |
| title | Classical Numerical Methods in Scientific Computing |
| title_full | Classical Numerical Methods in Scientific Computing |
| title_fullStr | Classical Numerical Methods in Scientific Computing |
| title_full_unstemmed | Classical Numerical Methods in Scientific Computing |
| title_short | Classical Numerical Methods in Scientific Computing |
| title_sort | classical numerical methods in scientific computing |
| topic | partial differential equations finite element method discretization time integration mathematical modelling thema EDItEUR::P Mathematics and Science::PB Mathematics::PBC Mathematical foundations |
| topic_facet | partial differential equations finite element method discretization time integration mathematical modelling thema EDItEUR::P Mathematics and Science::PB Mathematics::PBC Mathematical foundations |
| url | ONIX_20250522T133704_9789463667326_50 |
| work_keys_str_mv | AT vankanjos classicalnumericalmethodsinscientificcomputing AT segalguus classicalnumericalmethodsinscientificcomputing AT vermolenfred classicalnumericalmethodsinscientificcomputing |