An Explicit Sixth Order Runge-Kutta Method for Simple Lawson Integration
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915685671632896 |
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| author | Golden, Matthew |
| author_facet | Golden, Matthew |
| contents | Explicit Runge-Kutta schemes become impractical when a stiff linear operator is present in the dynamics. This failure mode is quite common in numerical simulations of fluids and plasmas. Lawson proposed Generalized Runge-Kutta Processes for stiff problems in 1967, in which the stiff linear operator is treated fully implicitly via matrix exponentiation. Any Runge-Kutta scheme induces valid Lawson integration, but a scheme is exceptionally simple to implement if the abscissa $c_i$ are ordered and equally spaced. Classical RK4 satisfies this requirement, but it is difficult to derive efficient higher order schemes with this constraint. Here I present an explicit sixth order method identified with Newton-Raphson iteration that provides simple Lawson integration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17006 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Explicit Sixth Order Runge-Kutta Method for Simple Lawson Integration Golden, Matthew Numerical Analysis Mathematical Physics Chaotic Dynamics Explicit Runge-Kutta schemes become impractical when a stiff linear operator is present in the dynamics. This failure mode is quite common in numerical simulations of fluids and plasmas. Lawson proposed Generalized Runge-Kutta Processes for stiff problems in 1967, in which the stiff linear operator is treated fully implicitly via matrix exponentiation. Any Runge-Kutta scheme induces valid Lawson integration, but a scheme is exceptionally simple to implement if the abscissa $c_i$ are ordered and equally spaced. Classical RK4 satisfies this requirement, but it is difficult to derive efficient higher order schemes with this constraint. Here I present an explicit sixth order method identified with Newton-Raphson iteration that provides simple Lawson integration. |
| title | An Explicit Sixth Order Runge-Kutta Method for Simple Lawson Integration |
| topic | Numerical Analysis Mathematical Physics Chaotic Dynamics |
| url | https://arxiv.org/abs/2512.17006 |