Pointwise-in-time error bounds for semilinear and quasilinear fractional subdiffusion equations on graded meshes

2025/06/15 by Natalia Kopteva, Kopteva, Natalia, Sean T. Kelly +1
Mathematics · Computer Science · #Differential Equations and Numerical Methods #Advanced Mathematical Modeling in Engineering #Fractional Differential Equations Solutions

paper · pdf · doi:10.48550/arxiv.2506.12954

Abstract

Time-fractional semilinear and quasilinear parabolic equations with a Caputo time derivative of order α∈(0,1) are considered, solutions of which exhibit a singular behaviour at an initial time of type t^σ for any fixed σ∈ (0,1) ∪ (1,2). The L1 scheme in time is combined with a general class of discretizations for the semilinear term. For such discretizations, we obtain sharp pointwise-in-time error bounds on graded temporal meshes with arbitrary degree of grading. Both semi-discretizations in time and full discretizations using finite differences and finite elements in space are addressed. The theoretcal findings are illustrated by numerical experiments.

Citations

• Error analysis of an L2-type method on graded meshes for semilinear subdiffusion equations
• Regularity Analysis and High-Order Time Stepping Scheme for Quasilinear Subdiffusion
• Sharp pointwise-in-time error estimate of L1 scheme for nonlinear subdiffusion equations
• Error analysis for time-fractional semilinear parabolic equations using upper and lower solutions
• Time-Fractional Allen-Cahn Equations: Analysis and Numerical Methods
• Error analysis of the L1 method on graded and uniform meshes for a\n fractional-derivative problem in two and three dimensions
• Numerical analysis of nonlinear subdiffusion equations

Related

• Error analysis of an L2-type method on graded meshes for semilinear subdiffusion equations
• Error analysis for time-fractional semilinear parabolic equations using upper and lower solutions
• Error analysis of an L2-type method on graded meshes for a fractional-order parabolic problem
• Galerkin Type Methods for Semilinear Time-Fractional Diffusion Problems
• Error analysis of the L1 method on graded and uniform meshes for a\n fractional-derivative problem in two and three dimensions