Unconditional convergence of linearized orthogonal spline collocation algorithm for semilinear subdiffusion equation with nonsmooth solution

Abstract

AbstractA linearized orthogonal spline collocation (OSC) method withC1splines of degree≥3on a suitable graded mesh is formulated and analyzed for approximate solution of an initial‐boundary‐value problem of semilinear subdiffusion equations with nonsmooth solutions in time. The sharp error estimate in theL2norm is established without any restriction on the relative temporal and spatial mesh sizes. Such unconditional convergence results are proved by including the typical singularity of the solution near the timet = 0. Results of numerical experiments support the analytical results.