Efficient high-order two-derivative DIRK methods with optimized phase errors
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912770804416512 |
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| author | Ehigie, Julius Luan, Vu Thai |
| author_facet | Ehigie, Julius Luan, Vu Thai |
| contents | This work constructs and analyzes new efficient high-order two-derivative diagonally implicit Runge--Kutta (TDDIRK) schemes with optimized phase errors. Specifically, we present a convergence result for TDDIRK methods and investigate their optimized phase errors and linear stability analysis. Based on these, we derive new families of 2-stage fourth-order, 2-stage fifth-order, and 3-stage fifth-order TDDIRK schemes. Finally, we provide numerical experiments at both the ODE and PDE levels to demonstrate the accuracy and efficiency of these new schemes compared to known DIRK schemes in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15227 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient high-order two-derivative DIRK methods with optimized phase errors Ehigie, Julius Luan, Vu Thai Numerical Analysis 65L05, 65M20 This work constructs and analyzes new efficient high-order two-derivative diagonally implicit Runge--Kutta (TDDIRK) schemes with optimized phase errors. Specifically, we present a convergence result for TDDIRK methods and investigate their optimized phase errors and linear stability analysis. Based on these, we derive new families of 2-stage fourth-order, 2-stage fifth-order, and 3-stage fifth-order TDDIRK schemes. Finally, we provide numerical experiments at both the ODE and PDE levels to demonstrate the accuracy and efficiency of these new schemes compared to known DIRK schemes in the literature. |
| title | Efficient high-order two-derivative DIRK methods with optimized phase errors |
| topic | Numerical Analysis 65L05, 65M20 |
| url | https://arxiv.org/abs/2512.15227 |