Solving Ordinary Differential Equations in Python

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