Solving Differential Equations in R
by Karline Soetaert, Jeff Cash and Francesca Mazzia
Published by Springer Press
The books’ package on CRAN is diffEq.
I happily read through this book on a Sunday afternoon. It is a straight forward book to use if you already understand differential equations and can program in R. If either topic is new to you , learn them first then tackle this book.
It is much easier to code Euler’s and Newton’s method in R than the C and FORTRAN the code I originally used for these methods.
My favorite bit of code is the Elastica Problem in Chapter 11. The problem is a system of five differential equations describing an elastica in the x,y plane. Uses package bvpSolve. The package for solving boundary value problems.
Figure 2.4 page 37 is a nice chart of the main Families of IVP, Initial Value Problems solutions.
This book gives you the tools you need to solve differential equations in R.