dopri45
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dopri45 [2019/11/18 13:34] 127.0.0.1 external edit |
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| ====== DOPRI45 ====== | ====== DOPRI45 ====== | ||
| - | Dormand-Prince | + | Dormand-Prince |
| - | Explicit one-step solver based on Runge-Kutta (4,5) pair of Dormand | + | In numerical analysis, the Dormand–Prince method or DOPRI method, is an embedded method for solving ordinary differential equations (Dormand & Prince 1980). The method is a member |
| Applicable for **non-stiff** problems of **medium** accuracy. | Applicable for **non-stiff** problems of **medium** accuracy. | ||
| Line 9: | Line 9: | ||
| The [[Butcher_tableau|Butcher tableau]] for the adaptive Dormand–Prince method is: | The [[Butcher_tableau|Butcher tableau]] for the adaptive Dormand–Prince method is: | ||
| - | 0 | + | |0| | | | | | | | |
| - | 1/5 | + | |1/5|1/5| | | | | | | |
| - | 1/5 | + | |3/10|3/40|9/40| | | | | | |
| - | 3/10 | + | |4/5|44/45|-56/15|32/9| | | | | |
| - | 3/40 | + | |8/9|19372/6561|-25360/2187|64448/6561|-212/ |
| - | 9/40 | + | |1|9017/3168|-355/33|46732/5247|49/176|−5103/18656| | | |
| - | 4/5 | + | |1|35/ |
| - | 44/45 | + | | |35/384|0|500/1113|125/192|−2187/6784|11/84 |0| |
| - | -56/15 | + | | |5179/57600|0|7571/16695|393/640|−92097/ |
| - | 32/9 | + | |
| - | 8/9 | + | |
| - | 19372/6561 | + | The first row of b coefficients gives the fifth-order accurate solution, and the second row gives the fourth-order accurate solution. |
| - | -25360/2187 | + | |
| - | 64448/6561 | + | |
| - | -212/729 | + | |
| - | 1 | + | |
| - | 9017/3168 | + | |
| - | -355/33 | + | |
| - | 46732/5247 | + | |
| - | 49/176 | + | |
| - | -5103/ | + | |
| - | 1 | + | |
| - | 35/384 | + | |
| - | 0 | + | |
| - | 500/1113 | + | |
| - | 125/192 | + | |
| - | -2187/6784 | + | |
| - | 11/84 | + | |
| - | 5179/57600 | + | |
| - | 0 | + | |
| - | 7571/16695 | + | |
| - | 393/640 | + | |
| - | -92097/ | + | |
| - | 187/2100 | + | |
| - | 1/40 | + | |
| - | 35/384 | + | |
| - | 0 | + | |
| - | 500/1113 | + | |
| - | 125/192 | + | |
| - | -2187/6784 | + | |
| - | 11/84 | + | |
| - | 0 | + | |
| Applicable [[Solver_settings|solver settings]]: | Applicable [[Solver_settings|solver settings]]: | ||
| Line 68: | Line 40: | ||
| * Dormand, J. R. and P. J. Prince, “A family of embedded Runge-Kutta formulae, | * Dormand, J. R. and P. J. Prince, “A family of embedded Runge-Kutta formulae, | ||
| + | * http:// | ||
dopri45.1574080453.txt.gz · Last modified: 2019/11/18 13:34 by 127.0.0.1
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