Crank-Nicolson schemes for sub-diffusion equations with nonsingular and singular source terms in time
Numerical Analysis
2024-01-23 v1 Numerical Analysis
Abstract
In this work, two Crank-Nicolson schemes without corrections are developed for sub-diffusion equations. First, we propose a Crank-Nicolson scheme without correction for problems with regularity assumptions only on the source term. Second, since the existing Crank-Nicolson schemes have a severe reduction of convergence order for solving sub-diffusion equations with singular source terms in time, we then extend our scheme and propose a new Crank-Nicolson scheme for problems with singular source terms in time. Second-order error estimates for both the two Crank-Nicolson schemes are rigorously established by a Laplace transform technique, which are numerically verified by some numerical examples.
Cite
@article{arxiv.2305.06138,
title = {Crank-Nicolson schemes for sub-diffusion equations with nonsingular and singular source terms in time},
author = {Han Zhou and Wenyi Tian},
journal= {arXiv preprint arXiv:2305.06138},
year = {2024}
}