p-ADAPTIVITY IN THE TIME DOMAIN USING MVpq MULTIVALUE TIME-MARCHING INTEGRATORS

A uniÞed set of MVpq multivalue algorithms for a single-step time-marching scheme is presented for the transient di¤usion equation. These MVpq algorithms include the well-known SSij single-step algorithms as a special case. Non-uniform integrators are introduced in which discrete equations in the o.d.e. set each separately use a di¤erent order of integrator. Hierarchical variables are used in the time domain, Þrstly to facilitate non-uniform integrators and secondly to permit variable length timesteps. This paper is the Þrst in a series. In the sequel (Part 2)17 error estimates are introduced and the non-uniform integrator concept is utilized to implement p-adaptivity in time