This method is described in H. A. Luther 1968 paper An explicit Sixth-Order Runge-Kutta Formula.
This method is an explicit Runge-Kutta method, its Butcher-array is the following one :
0 | 0 0 0 0 0 0
1 | 1 0 0 0 0 0
1/2 | 3/8 1/8 0 0 0 0
2/3 | 8/27 2/27 8/27 0 0 0
(7-q)/14 | ( -21 + 9q)/392 ( -56 + 8q)/392 ( 336 - 48q)/392 ( -63 + 3q)/392 0 0
(7+q)/14 | (-1155 - 255q)/1960 ( -280 - 40q)/1960 ( 0 - 320q)/1960 ( 63 + 363q)/1960 ( 2352 + 392q)/1960 0
1 | ( 330 + 105q)/180 ( 120 + 0q)/180 ( -200 + 280q)/180 ( 126 - 189q)/180 ( -686 - 126q)/180 ( 490 - 70q)/180
|--------------------------------------------------------------------------------------------------------------------------------------------------
| 1/20 0 16/45 0 49/180 49/180 1/20
where q = √21
EulerIntegrator, ClassicalRungeKuttaIntegrator, GillIntegrator, MidpointIntegrator, ThreeEighthesIntegrator
| Modifier and Type | Field and Description |
|---|---|
| private static final double | Q
Square root. |
| private static final double[][] | STATIC_A
Internal weights Butcher array. |
| private static final double[] | STATIC_B
Propagation weights Butcher array. |
| private static final double[] | STATIC_C
Time steps Butcher array. |
| Access | Constructor and Description |
|---|---|
| public |
| Q | back to summary |
|---|---|
| private static final double Q Square root. | |
| STATIC_A | back to summary |
|---|---|
| private static final double[][] STATIC_A Internal weights Butcher array. | |
| STATIC_B | back to summary |
|---|---|
| private static final double[] STATIC_B Propagation weights Butcher array. | |
| STATIC_C | back to summary |
|---|---|
| private static final double[] STATIC_C Time steps Butcher array. | |
| LutherIntegrator | back to summary |
|---|---|
| public LutherIntegrator(final double step) Simple constructor. Build a fourth-order Luther integrator with the given step.
| |