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Unconditional convergence of linearized orthogonal spline collocation algorithm for semilinear subdiffusion equation with nonsmooth solution
Author(s) -
Zhang Haixiang,
Yang Xuehua,
Xu Da
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22583
Subject(s) - mathematics , convergence (economics) , norm (philosophy) , spline (mechanical) , collocation (remote sensing) , singularity , mathematical analysis , orthogonal collocation , collocation method , boundary value problem , differential equation , computer science , ordinary differential equation , political science , law , machine learning , structural engineering , engineering , economics , economic growth
A linearized orthogonal spline collocation (OSC) method with C 1 splines of degree ≥3 on 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 the L 2 norm 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 time t = 0 . Results of numerical experiments support the analytical results.