A Second-Order Scheme with Nonuniform Time Steps for a Linear Reaction-Subdiffusion Problem

Stability and convergence of a time-weighted discrete scheme with nonuniform time steps are established for linear reaction-subdiffusion equations. The Caupto derivative is approximated at an offset point by using quadratic polynomial interpolation. Our analysis relies on two tools: fractional Gr\"{o}nwall inequality the global consistency analysis. new makes use interpolation error formula polynomials, which leads to convolution-type bound local truncation error. To exploit these tools, some theoretical properties kernels in numerical Caputo crucial we investigate them intensively setting. Taking initial singularity solution into account, obtain sharp estimate meshes. fully generates second-order accurate graded mesh provided proper grading parameter employed. An example presented show sharpness our