Sharp <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e2749" altimg="si4.svg"><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math>-norm error estimates of two time-stepping schemes for reaction–subdiffusion problems

Due to the intrinsically initial singularity of solution and discrete convolution form in numerical Caputo derivatives, traditional H1-norm analysis (corresponding case for a classical diffusion equation) time approximations fractional subdiffusion problem always leads suboptimal error estimates (a loss accuracy). To recover theoretical accuracy time, we propose an improved Grönwall inequality apply it well-known L1 formula Crank–Nicolson scheme. With help time-space error-splitting technique global consistency analysis, sharp two nonuniform approaches are established reaction–subdiffusion problems. Numerical experiments included confirm sharpness our analysis.