Abstract
We analyze a single step method for solving second-order parabolic initial--boundary value problems. The method uses a step-doubling extrapolation scheme in time based on backward Euler and a Galerkin approximation in space. The technique is shown to be a second-order correct approximation in time. Since step-doubling can be used as a mechanism for step-size control, the analysis is done for variable time steps. The stability properties of step-doubling are contrasted with t hose of Crank-Nicolson, and more generally those of extrapolated theta-weighted schemes.
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