ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
In this paper we extend predictor-corrector methods, commonly used for the numerical solution of ordinary differential equations (o.d.e.s), to parabolic partial differential equations (p.d.e.s), typically of the form ut = auxx + ƒ(u, ux, x, t).We describe linear multistep methods for p.d.e.s, the nonlinear algebraic equations arising from implicit formulae being solved using a corrector analogous to those used for o.d.e.s. A sufficient condition for convergence of the iteration is then derived and is found, in most cases, to be far less restrictive than that obtained from the usual method of lines approach. Numerical results are presented to investigate the necessity of this condition. They also indicate that we can accelerate convergence by reducing the time increment. This allows us to achieve convergence within a prescribed number of iterations and so to construct PCm methods corresponding to P(EC)m methods for o.d.e.s. Numerical results are also given to test the absolute stability of the Crank-Nicolson corrector for various predictors P, and iterations, m.
Additional Material:
10 Tab.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620190311
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