Matrix time-extrapolation algorithm for solving semilinear parabolic problems

Abstract 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 + 2 p to construct quadratic interpolation so that we can estimate matrix values at levels m + 2 p + 1 , m + 2 p + 2 , … , m + 3 p − 1 , then the matrix value is recalculated at the level m + 3 p . 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.

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