## ABSTRACT

In Chapter 1, a basic moving boundary partial differential equation (MBPDE) system, eqs. (1.2) through (1.6), is developed to test a MBPDE algorithm. The algorithm is implemented in Chapter 2 as a set of R routines. The output from the R routines is now considered in Chapter 3 for a series of cases, ncase=1,2,3.

ncase=1: The equation of motion of eqs. (1.5) and (1.6) defines a zero movement (velocity) so that the outer radial boundary condition (BC) does not move. The resulting solution is confirmed by a conventional method of lines (MOL) implementation based on spline approximations in Appendix A1 and a MOL implementation based on finite differentiation (FD) approximations in Appendxix A2.

ncase=2: The outer radial boundary moves at a constant velocity and is conformed by the graphical output for the boundary position and velocity.

ncase=3: The outer radial boundary moves at a rate (velocity) defined by the mass transfer rate of eq. (1.6).

The variation of the parameters for ncase=1,2,3 is detailed in eight sets of plots and a discussion of the effect of the moving boundary.