An iterative method is presented and analyzed which is based on using a preconditioned conjugate gradient iteration for approximately solving the linear equations produced at each time step by an extrapolated Crank–Nicolson–Galerkin procedure for time-stepping a quasilinear parabolic problem. Optimal order convergence rates are obtained for the iterative method which is shown to be (asymptotically) computationally more efficient than standard second-order-in-time correct methods.
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Douglas et al. (1979) studied this question.
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