Solving Ordinary Differential Equations in Python / by Joakim Sundnes.

Format:

Book

Author/Creator:

Sundnes, Joakim.

Series:

Simula SpringerBriefs on Computing, 2512-1685 ; 15

Language:

English

Subjects (All):

Mathematics--Data processing.

Mathematics.

Computer science.

Computational Science and Engineering.

Computer Science.

Local Subjects:

Computational Science and Engineering.

Computer Science.

Mathematics.

Physical Description:

1 online resource (124 pages)

Edition:

1st ed. 2024.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2024.

Summary:

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.

Contents:

Preface

Programming a Simple ODE Solver

Improving the Accuracy

Stable Solvers for Stiff ODE Systems

Adaptive Time Step Methods

Modeling Infectious Diseases

Programming of Difference Equations

References

Index.

Other Format:

Print version: Sundnes, Joakim Solving Ordinary Differential Equations in Python

ISBN:

3-031-46768-X

OCLC:

1409679921