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Автор: Joakim Sundnes
Издательство: Springer
Год: 2024
Страниц: 124
Язык: английский
Формат: pdf (true), djvu
Размер: 10.2 MB
This book 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. The main purpose of the notes is to serve as a concise and gentle introduction to solving differential equations in Python, specifically for the course Introduction to programming for scientific applications (IN1900, 10 ETCS credits) at the University of Oslo. These notes will be most useful for readers with a basic knowledge of Python and NumPy, and it is also useful to have a fundamental understanding of ODEs.