Matrix time-extrapolation algorithm for solving semilinear parabolic problems

In this letter, we propose a fast matrix time-extrapolation algorithm to solve semilinear parabolic problems of Crank-Nicolson-based finite element scheme, which employs exact matrix values computed by integral at time levels m, m+p, m+2p to construct quadratic interpolation so that we can estimate matrix values at levels m+2p+1,m+2p+2,…,m+3p−1, then the matrix value is recalculated at the level m+3p. This process is performed iteratively, and finally, the calculation for matrices decreases to 1∕p. The error estimate of this algorithm is proven, and numerical examples are established to support this theory.