Initial Value Problems for Ordinary Differential Equations

6. Initial Value Problems for Ordinary Differential Equations#

This chapter was last revised on November 10, 2025; see An Introduction to Multistep Methods: Leap-frog

References:

[Chasnov, 2012] Chapter 7, Ordinary differential equations.
[Sullivan, 2021] Chapter 5, Ordinary Differential Equations
[Sauer, 2022] Chapter 6 Ordinary Differential Equations.
[Burden et al., 2016] Chapter 5 Initial-Value Problems for Ordinary Differential Equations.
[Chenney and Kincaid, 2013] Chapter 7, Initial-Value Problems, Sections 2 to 5.
[Dionne, 2023] Chapter 13, Initial-Value Problems.
[Kincaid and Chenney, 1990] Chapter 8, Numerical Solution of Ordinary Differential Equations, Sections 0 to 6.
[Vuik et al., 2015] Numerical Methods for Ordinary Differential Equations.
[LeVeque, 2007] Finite Difference Methods for Ordinary and Partial Differential Equations, Chapters 5 to 8.
[Dahlquist and Björck, 2008] Section 1.4, Numerical Solution of Differential Equations.
MIT Open Courseware notes on solving ODE IVP’s

Randall LeVeque