An efficient acceleration technique of implicit schemes for quasi-linear parabolic problems

An efficient acceleration technique based on high-order time extrapolation method is proposed to construct a good initial guess for the iterative solution of implicit schemes for solving two-dimensional quasi-linear parabolic equations. Compared with traditional methods, the new algorithm has obvious advantage in reducing the number of Picard iterations by 2/3 to 6/7. One of the high-order formulas labelled as 5D6L requires only one nonlinear iteration for most testing cases. The smaller the time step is, the better the acceleration effect of the new algorithm. Numerical results are presented to verify the effectiveness of the proposed method.