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Explicit multistep methods for nonstiff partial differential equations

✍ Scribed by Panagiotis Chatzipantelidis

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
890 KB
Volume
27
Category
Article
ISSN
0168-9274

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✦ Synopsis

We approximate the solution of initial boundary value problems for equations of the form Au'(t) =: B(t, u(t)), t E [0, t*]. A is a linear, selfadjoint, positive definite operator on a Hilbert space (H, (-, .)) and B is a possibly nonlinear operator. We discretize in space by finite element methods and for the time discretization we use explicit linear multistep schemes. We derive optimal order error estimates. The abstract results are applied to the Rosenau equation in R", m <~ 3, to a generalized Sobolev equation in one space dimension, to a pseudoparabolic equation in ]~'", m = 2, 3, and to a system of equations of Boussinesq type.

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