The Euler algorithm is the simplest one that can be used to
integrate ordinary differential equations. It is a simple inversion
of the forward difference expression :
f'=(f(t+h)-f(t))/h which leads to
f(t+h)=f(t)+hf'. The interpolation scheme used for
dense output is the linear scheme already used for integration.
This algorithm looks cheap because it needs only one function evaluation per step. However, as it uses linear estimates, it needs very small steps to achieve high accuracy, and small steps lead to numerical errors and instabilities.
This algorithm is almost never used and has been included in this package only as a comparison reference for more useful integrators.
MidpointFieldIntegrator, ClassicalRungeKuttaFieldIntegrator, GillFieldIntegrator, ThreeEighthesFieldIntegrator, LutherFieldIntegrator
| Access | Constructor and Description |
|---|---|
| public | EulerFieldIntegrator(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 EulerFieldStepInterpolator | 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). |
| EulerFieldIntegrator | back to summary |
|---|---|
| public EulerFieldIntegrator(final Field<T> field, final T step) Simple constructor. Build an Euler integrator with the given step.
| |
| createInterpolator | back to summary |
|---|---|
| protected EulerFieldStepInterpolator 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).
| |