Explicit multistep methods for nonstiff partial differential equations (Q1294583)

An approximate solution of initial-boundary value problems is considered for equations of the form \(Au'(t)= B(t,u(t))\), where \(A\) is a linear, selfadjoint, positive definite operator on a Hilbert space and \(B\) is a possibly nonlinear operator. The problem is discretized in space by finite element methods, and for the time discretization explicit linear multistep schemes are applied. Optimal order error estimates are derived. The abstract results are used to the Rosenau equation, a genealized Sobolev equation, a pseudoparabolic equation and a system of equations of Boussinesq type.