Crank-Nicolson schemes for sub-diffusion equations with nonsingular and singular source terms in time
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916099158704128 |
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| author | Zhou, Han Tian, Wenyi |
| author_facet | Zhou, Han Tian, Wenyi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06138 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Crank-Nicolson schemes for sub-diffusion equations with nonsingular and singular source terms in time Zhou, Han Tian, Wenyi Numerical Analysis 65M06, 65M60, 65M15, 35R11, 35R05 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. |
| title | Crank-Nicolson schemes for sub-diffusion equations with nonsingular and singular source terms in time |
| topic | Numerical Analysis 65M06, 65M60, 65M15, 35R11, 35R05 |
| url | https://arxiv.org/abs/2305.06138 |