An efficient class of discrete finite difference/element scheme for solving the fractional reaction subdiffusion equation

摘要

An estimate for the fractional reaction subdiffusion equation is presented by a discrete Crank–Nicolson finite element method (FEM), which we can obtain by using the finite difference method (FDM) (in time) and the finite element method (in space). The proposed scheme is obtained at time tn+12$$ {t}_{namp;amp;amp;amp;amp;#x0002B;frac{1}{2}} $$ because at this time there are some different coefficients compared to those at time tn+1$$ {t}_{namp;amp;amp;amp;amp;#x0002B;1} $$, that is, k+121−β−k−121−β$$ left({left(kamp;amp;amp;amp;amp;#x0002B;frac{1}{2}right)}amp;amp;amp;amp;amp;#x0005E;{1-beta }-{left(k-frac{1}{2}right)}amp;amp;amp;amp;amp;#x0005E;{1-beta}right) $$, instead of (k+1)1−β−(k)1−β$$ left({left(kamp;amp;amp;amp;amp;#x0002B;1right)}amp;amp;amp;amp;amp;#x0005E;{1-beta }-{(k)}amp;amp;amp;amp;amp;#x0005E;{1-beta}right) $$. We studied the stability analysis, truncation error, and convergence analysis of the derived scheme. Numerical examples are presented to illustrate the efficiency of the given algorithm.