Solutions to ODEs and PDEs: Numerical analysis using R

The solution of ordinary differential equations (ODEs) is intrinsically bound up with the solution of partial differential equations (PDEs). In this chapter the basic integration methods are introduced, covering: Euler, Runge-Kutta, variable step, extrapolation, BDFs, NDFs, and Adams. Various test examples for the different integration methods are provided along with annotated code. The Newton and Levenberg-Marquardt convergence methods are introduced with practical examples of use in implicit numerical integration, together with the corresponding computer code. A discussions relating to truncation error and verification of integration order are presented with examples. The chapter concludes with a brief discussion on stiffness. All the computer code discussed in the text is available for download.