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arXiv · 2305.06138

Crank-Nicolson schemes for sub-diffusion equations with nonsingular and singular source terms in time

Han Zhou·Wenyi Tian
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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.

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Han Zhou, Wenyi Tian. 2023-05-10. Crank-Nicolson schemes for sub-diffusion equations with nonsingular and singular source terms in time. https://doi.org/10.1007/s10915-023-02442-9

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