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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.00594 |
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| _version_ | 1866914361205850112 |
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| author | Hu, Xianfa Geng, Fazhan Wang, Wansheng |
| author_facet | Hu, Xianfa Geng, Fazhan Wang, Wansheng |
| contents | In this paper, we consider the integrating factor midpoint method for wave-type equations and derive optimal order a posteriori error estimates. We first introduce an integrating factor midpoint approximation defined by the piecewise linear approximate solutions, and derive suboptimal order residual-based error estimates using the energy technique. Hence the key is introducing a continuous, piecewise quadratic time reconstruction to establish optimal order error bounds. Based on the reliable a posteriori error control, we develop an adaptive time-stepping strategy. Numerical examples are implemented to verify the convergence rate of an error estimator and the high efficiency of the adaptive algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00594 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An adaptive integrating factor midpoint method for second order evolution equations Hu, Xianfa Geng, Fazhan Wang, Wansheng Numerical Analysis In this paper, we consider the integrating factor midpoint method for wave-type equations and derive optimal order a posteriori error estimates. We first introduce an integrating factor midpoint approximation defined by the piecewise linear approximate solutions, and derive suboptimal order residual-based error estimates using the energy technique. Hence the key is introducing a continuous, piecewise quadratic time reconstruction to establish optimal order error bounds. Based on the reliable a posteriori error control, we develop an adaptive time-stepping strategy. Numerical examples are implemented to verify the convergence rate of an error estimator and the high efficiency of the adaptive algorithm. |
| title | An adaptive integrating factor midpoint method for second order evolution equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2603.00594 |