Explicit multistep methods for nonstiff partial differential equations Original Research Article

We approximate the solution of initial boundary value problems for equations of the form Au′(t) = B(t,u(t)), t ∈ [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 View the MathML sourcem, m ≤ 3, to a generalized Sobolev equation in one space dimension, to a pseudoparabolic equation in View the MathML sourcem, m = 2,3, and to a system of equations of Boussinesq type.