P-ADAPTIVITY IN THE TIME-DOMAIN USING MVPQ MULTIVALUE TIME-MARCHING INTEGRATORS

A unified set of MVpq multivalue algorithms for a single-step time-mar ching scheme is presented for the transient diffusion equation. These MVpq algorithms include the well-known SSij single-step algorithms as a special case. Non-uniform integrators are introduced in which discre te equations in the o.d.e. set each separately use a different order o f integrator. Hierarchical variables are used in the time domain, firs tly to facilitate non-uniform integrators and secondly to permit varia ble length timesteps. This paper is the first in a series. In the sequ el (Part 2)(17) error estimates are introduced and the non-uniform int egrator concept is utilized to implement p-adaptivity in time. (C) 199 7 by John Wiley & Sons, Ltd.