The role of initial value solvers in a moving mesh method

This thesis investigates the role of different initial value solvers in moving mesh software for solving second-order parabolic partial differential equations. We confine our attention primarily to the effect of the implicit ODE solver DDASSL used in the software MOVCOL of Huang and Russell, which is based on a moving collocation method. The advantages and limitations of Backward Differentiation Formula (BDF) methods and Implicit Runge-Kutta (IRK) methods are discussed in this particular context and the alternative ODE solver PSIDE, which is based on a four-stage RADAU IIA algorithm, is examined. The new interface of PSIDE with MOVCOL is discussed in some detail. Its performance is compared with DDASSL for several numerical problems.