Unconditional convergence of linearized orthogonal spline collocation algorithm for semilinear subdiffusion equation with nonsmooth solution
Haixiang Zhang, Xuehua Yang, Da Xu
Abstract
Abstract 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.
Topics & Concepts
MathematicsConvergence (economics)Norm (philosophy)Spline (mechanical)Collocation (remote sensing)Applied mathematicsSingularityMathematical analysisOrthogonal collocationCollocation methodBoundary value problemDifferential equationComputer scienceLawOrdinary differential equationEconomic growthEngineeringPolitical scienceMachine learningStructural engineeringEconomicsDifferential Equations and Numerical MethodsFractional Differential Equations SolutionsIterative Methods for Nonlinear Equations