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Feature: Update default ARKODE methods (#547)
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Update the default RK tables in ARKODE:
- ARK order >2: Follows the recommendations in the conclusion of
https://doi.org/10.1016/j.apnum.2018.10.007
- ERK order 4: Improved principal error and embedded quality metrics
- ERK order 5: Improved principal error and embedded quality metrics
- ERK order 8: Switch to a method designed for local extrapolation mode,
likely better principal error.
- DIRK order 2: Improved principal error, L-stability, and stage order 2
- DIRK order >2: Follows the recommendations in the conclusion of
https://doi.org/10.1016/j.apnum.2019.07.008

---------

Co-authored-by: David Gardner <gardner48@llnl.gov>
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Steven-Roberts and gardner48 authored Feb 12, 2025
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19 changes: 19 additions & 0 deletions CHANGELOG.md
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### New Features and Enhancements

Added the `ARKODE_RALSTON_3_1_2` and `ARKODE_TSITOURAS_7_4_5` explicit
Runge-Kutta Butcher tables.

Improved the efficiency of default ARKODE methods with the following changes:

| Type | Old Default | New Default |
| ------------------ | ---------------------------------------------------------------- | ------------------------------------------------------------------ |
| 2nd Order Explicit | `ARKODE_HEUN_EULER_2_1_2` | `ARKODE_RALSTON_3_1_2` |
| 4th Order Explicit | `ARKODE_ZONNEVELD_5_3_4` | `ARKODE_SOFRONIOU_SPALETTA_5_3_4` |
| 5th Order Explicit | `ARKODE_CASH_KARP_6_4_5` | `ARKODE_TSITOURAS_7_4_5` |
| 6th Order Explicit | `ARKODE_VERNER_8_5_6` | `ARKODE_VERNER_9_5_6` |
| 8th Order Explicit | `ARKODE_FEHLBERG_13_7_8` | `ARKODE_VERNER_13_7_8` |
| 2nd Order Implicit | `ARKODE_SDIRK_2_1_2` | `ARKODE_ARK2_DIRK_3_1_2` |
| 3rd Order Implicit | `ARKODE_ARK324L2SA_DIRK_4_2_3` | `ARKODE_ESDIRK325L2SA_5_2_3` |
| 4th Order Implicit | `ARKODE_SDIRK_5_3_4` | `ARKODE_ESDIRK436L2SA_6_3_4` |
| 5th Order Implicit | `ARKODE_ARK548L2SA_DIRK_8_4_5` | `ARKODE_ESDIRK547L2SA2_7_4_5` |
| 4th Order ARK | `ARKODE_ARK436L2SA_ERK_6_3_4` and `ARKODE_ARK436L2SA_DIRK_6_3_4` | `ARKODE_ARK437L2SA_ERK_7_3_4` and `ARKODE_ARK437L2SA_DIRK_7_3_4` |
| 5th Order ARK | `ARKODE_ARK548L2SA_ERK_8_4_5` and `ARKODE_ARK548L2SA_DIRK_8_4_5` | `ARKODE_ARK548L2SAb_ERK_8_4_5` and `ARKODE_ARK548L2SAb_DIRK_8_4_5` |

### Bug Fixes

Fixed bug in `ARKodeSetFixedStep` where it could return `ARK_SUCCESS` despite
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