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oapen-20.500.12657-850812023-11-15T09:17:26Z Solving Ordinary Differential Equations in Python Sundnes, Joakim Ordinary differential equations Runge-Kutta methods scientific programming Python programming object-oriented programming difference equations adaptive time step methods bic Book Industry Communication::P Mathematics & science::PD Science: general issues::PDE Maths for scientists bic Book Industry Communication::U Computing & information technology::UY Computer science bic Book Industry Communication::P Mathematics & science::PB Mathematics This open access volume explains the foundations of modern solvers for ordinary differential equations (ODEs). Formulating and solving ODEs is an essential part of mathematical modeling and computational science, and numerous solvers are available in commercial and open source software. However, no single ODE solver is the best choice for every single problem, and choosing the right solver requires fundamental insight into how the solvers work. This book will provide exactly that insight, to enable students and researchers to select the right solver for any ODE problem of interest, or implement their own solvers if needed. The presentation is compact and accessible, and focuses on the large and widely used class of solvers known as Runge-Kutta methods. Explicit and implicit methods are motivated and explained, as well as methods for error control and automatic time step selection, and all the solvers are implemented as a class hierarchy in Python. 2023-11-13T16:42:26Z 2023-11-13T16:42:26Z 2024 book ONIX_20231113_9783031467684_32 9783031467684 9783031467677 https://library.oapen.org/handle/20.500.12657/85081 eng Simula SpringerBriefs on Computing application/pdf n/a 978-3-031-46768-4.pdf https://link.springer.com/978-3-031-46768-4 Springer Nature Springer Nature Switzerland 10.1007/978-3-031-46768-4 10.1007/978-3-031-46768-4 6c6992af-b843-4f46-859c-f6e9998e40d5 eb9ac1c9-bf74-4c3a-b0a2-e945a77d7280 9783031467684 9783031467677 Springer Nature Switzerland 15 114 Cham [...] open access
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OAPEN
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DSpace
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| language |
English
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| description |
This open access volume explains the foundations of modern solvers for ordinary differential equations (ODEs). Formulating and solving ODEs is an essential part of mathematical modeling and computational science, and numerous solvers are available in commercial and open source software. However, no single ODE solver is the best choice for every single problem, and choosing the right solver requires fundamental insight into how the solvers work. This book will provide exactly that insight, to enable students and researchers to select the right solver for any ODE problem of interest, or implement their own solvers if needed. The presentation is compact and accessible, and focuses on the large and widely used class of solvers known as Runge-Kutta methods. Explicit and implicit methods are motivated and explained, as well as methods for error control and automatic time step selection, and all the solvers are implemented as a class hierarchy in Python.
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| title |
978-3-031-46768-4.pdf
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| spellingShingle |
978-3-031-46768-4.pdf
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| title_short |
978-3-031-46768-4.pdf
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| title_full |
978-3-031-46768-4.pdf
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| title_fullStr |
978-3-031-46768-4.pdf
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| title_full_unstemmed |
978-3-031-46768-4.pdf
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978-3-031-46768-4.pdf
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Springer Nature
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2023
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https://link.springer.com/978-3-031-46768-4
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1799945221767692288
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