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.