These methods are explicit Runge-Kutta methods, their Butcher arrays are as follows :
0 |
c2 | a21
c3 | a31 a32
... | ...
cs | as1 as2 ... ass-1
|--------------------------
| b1 b2 ... bs-1 bs
EulerFieldIntegrator, ClassicalRungeKuttaFieldIntegrator, GillFieldIntegrator, MidpointFieldIntegrator
| Modifier and Type | Field and Description |
|---|---|
| private final T[][] | a
Internal weights from Butcher array (without the first empty row). |
| private final T[] | b
External weights for the high order method from Butcher array. |
| private final T[] | c
Time steps from Butcher array (without the first zero). |
| private final T | step
Integration step. |
| Access | Constructor and Description |
|---|---|
| protected | RungeKuttaFieldIntegrator(final Field<T>
field to which the time and state vector elements belong field, final String name of the method name, final T integration step step)Simple constructor. |
| Modifier and Type | Method and Description |
|---|---|
| protected abstract RungeKuttaFieldStepInterpolator | Returns: external weights for the high order method from Butcher arrayintegration 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, FieldEquationsMapper<T> equations mapper for the all equations mapper)Create an interpolator. |
| protected T | Returns: p/q computed in the instance fieldnumerator p, final int denominator q)Create a fraction. |
| public FieldODEStateAndDerivative | integrate(final FieldExpandableODE<T>
differential equations to integrate equations, final FieldODEState<T> initial state (time, primary and secondary state vectors) initialState, final T target time for the integration
(can be set to a value smaller than finalTime)t0 for backward integration)Implements org. Integrate the differential equations up to the given time. |
| public T[] | Returns: state vector attdifferential equations to integrate equations, final T initial time t0, final T[] initial value of the state vector at t0 y0, final T target time for the integration
(can be set to a value smaller than t)t0 for backward integration)Fast computation of a single step of ODE integration. |
| a | back to summary |
|---|---|
| private final T[][] a Internal weights from Butcher array (without the first empty row). | |
| b | back to summary |
|---|---|
| private final T[] b External weights for the high order method from Butcher array. | |
| c | back to summary |
|---|---|
| private final T[] c Time steps from Butcher array (without the first zero). | |
| step | back to summary |
|---|---|
| private final T step Integration step. | |
| RungeKuttaFieldIntegrator | back to summary |
|---|---|
| protected RungeKuttaFieldIntegrator(final Field<T> field, final String name, final T step) Simple constructor. Build a Runge-Kutta integrator with the given step. The default step handler does nothing. | |
| createInterpolator | back to summary |
|---|---|
| protected abstract RungeKuttaFieldStepInterpolator Create an interpolator.
| |
| fraction | back to summary |
|---|---|
| protected T fraction(final int p, final int q) Create a fraction.
| |
| integrate | back to summary |
|---|---|
| public FieldODEStateAndDerivative Implements org. Doc from org. Integrate the differential equations up to the given time. This method solves an Initial Value Problem (IVP). Since this method stores some internal state variables made
available in its public interface during integration (
| |
| singleStep | back to summary |
|---|---|
| public T[] singleStep(final FirstOrderFieldDifferentialEquations<T> equations, final T t0, final T[] y0, final T t) Fast computation of a single step of ODE integration. This method is intended for the limited use case of very fast computation of only one step without using any of the rich features of general integrators that may take some time to set up (i.e. no step handlers, no events handlers, no additional states, no interpolators, no error control, no evaluations count, no sanity checks ...). It handles the strict minimum of computation, so it can be embedded in outer loops.
This method is not used at all by the As this method does not use any of the state-dependent features of the integrator, it should be reasonably thread-safe if and only if the provided differential equations are themselves thread-safe.
| |