Chapter 2 is based on the partial differential equation (PDE) in 1D cylindrical coordinates with a moving outer boundary condition (BC) developed in Chapter 1 (MBPDE). The numerical solution of the MBPDE system is programmed in R as a main program and subordinate routine. 1

The subordinate routine implements the solution of the MBPDE system by the method of lines (MOL), a general algorithm for the integration (solution) of PDEs in which the PDE is replaced by an approximating system of initial-value ordinary differential equations (ODEs). The ODE system is integrated by a library initial-value ODE integrator available in the R system.

The R routines are discussed in detailed, particularly as related to the MBPDE system from Chapter 1. The routines are also available as a download which the reader/analyst/researcher can execute to produce the numerical solutions presented in Chapter 3.