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p ‐ADAPTIVITY IN THE TIME DOMAIN USING MV pq MULTIVALUE TIME‐MARCHING INTEGRATORS
Author(s) -
CAMPBELL JOHN S.,
ROBINSON JAMES C.
Publication year - 1997
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19970715)40:13<2343::aid-nme167>3.0.co;2-v
Subject(s) - integrator , set (abstract data type) , algorithm , time domain , domain (mathematical analysis) , computer science , transient (computer programming) , mathematics , variable (mathematics) , mathematical optimization , mathematical analysis , computer network , bandwidth (computing) , computer vision , programming language , operating system
A unified set of MV pq multivalue algorithms for a single‐step time‐marching scheme is presented for the transient diffusion equation. These MV pq algorithms include the well‐known SS ij 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 different order of integrator. Hierarchical variables are used in the time domain, firstly to facilitate non‐uniform integrators and secondly to permit variable length timesteps. This paper is the first 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. © 1997 by John Wiley & Sons, Ltd.