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
EulerFieldIntegrator, ClassicalRungeKuttaFieldIntegrator, GillFieldIntegrator, MidpointFieldIntegrator, ThreeEighthesFieldIntegrator
| Access | Constructor and Description |
|---|---|
| public | LutherFieldIntegrator(final Field<T>
field to which the time and state vector elements belong field, final T integration step step)Simple constructor. |
| Modifier and Type | Method and Description |
|---|---|
| protected LutherFieldStepInterpolator | createInterpolator(final boolean
integration direction indicator forward, T[][] slopes at the intermediate points yDotK, final FieldODEStateAndDerivative<T> start of the global step globalPreviousState, final FieldODEStateAndDerivative<T> end of the global step globalCurrentState, final FieldEquationsMapper<T> equations mapper for the all equations mapper)Implements abstract org. Create an interpolator. |
| public T[][] | getA()
Implements org. Get the internal weights from Butcher array (without the first empty row). |
| public T[] | getB()
Implements org. Get the external weights for the high order method from Butcher array. |
| public T[] | getC()
Implements org. Get the time steps from Butcher array (without the first zero). |
| LutherFieldIntegrator | back to summary |
|---|---|
| public LutherFieldIntegrator(final Field<T> field, final T step) Simple constructor. Build a fourth-order Luther integrator with the given step.
| |
| createInterpolator | back to summary |
|---|---|
| protected LutherFieldStepInterpolator Implements abstract org. Doc from org. Create an interpolator.
| |
| getA | back to summary |
|---|---|
| public T[][] getA() Implements org. Doc from org. Get the internal weights from Butcher array (without the first empty row).
| |
| getB | back to summary |
|---|---|
| public T[] getB() Implements org. Doc from org. Get the external weights for the high order method from Butcher array.
| |
| getC | back to summary |
|---|---|
| public T[] getC() Implements org. Doc from org. Get the time steps from Butcher array (without the first zero).
| |