Solving Ordinary Differential Equations in Python.

• Superior document: Simula SpringerBriefs on Computing Series ; v.15
• Author: Sundnes, Joakim.
• Place / Publishing House: Cham : : Springer,, 2023.; Ã2024.
• Year of Publication: 2023
• Edition: 1st ed.
• Language: English
• Series: Simula SpringerBriefs on Computing Series
• Physical Description: 1 online resource (124 pages)

Table of Contents

• Intro
• Series Foreword
• Preface
• Contents
• Chapter 1 Programming a Simple ODE Solver
• 1.1 Creating a General-Purpose ODE Solver
• 1.2 The ODE Solver Implemented as a Class
• 1.3 Systems of ODEs
• 1.4 A ForwardEuler Class for Systems of ODEs
• 1.5 Checking the Error in the Numerical Solution
• 1.6 Using ODE Solvers from SciPy
• Chapter 2 Improving the Accuracy
• 2.1 Explicit Runge-Kutta Methods
• 2.2 A Class Hierarchy of Runge-Kutta Methods
• 2.3 Testing the Solvers
• Chapter 3 Stable Solvers for Stiff ODE Systems
• 3.1 Stiff ODE Systems and Stability
• 3.2 Implicit methods for stability
• 3.3 Implementing Implicit Runge-Kutta Methods
• 3.4 Implicit Methods of Higher Order
• 3.4.1 Fully Implicit RK Methods
• 3.4.2 Diagonally Implicit RK Methods
• 3.5 Implementing Higher Order IRK Methods
• 3.5.1 A Base Class for Fully Implicit Methods
• 3.5.2 Base Classes for SDIRK and ESDIRK Methods
• Chapter 4 Adaptive Time Step Methods
• 4.1 A Motivating Example
• 4.2 Choosing the Time Step Based on the Local Error
• 4.3 Estimating the Local Error
• 4.3.1 Error Estimates from Embedded Methods
• 4.4 Implementing an Adaptive Solver
• 4.5 More Advanced Embedded RK Methods
• Chapter 5 Modeling Infectious Diseases
• 5.1 Derivation of the SIR model
• 5.2 Extending the SIR Model
• 5.3 A Model of the Covid-19 Pandemic
• Appendix A Programming of Difference Equations
• A.1 Sequences and Difference Equations
• A.2 More Examples of Difference Equations
• A.3 Systems of Difference Equations
• A.4 Taylor Series and Approximations
• References
• Index.