This abstract class holds the common part of all adaptive stepsize integrators for Ordinary Differential Equations.
These algorithms perform integration with stepsize control, which means the user does not specify the integration step but rather a tolerance on error. The error threshold is computed as
threshold_i = absTol_i + relTol_i * max (abs (ym), abs (ym+1))
where absTol_i is the absolute tolerance for component i of the state vector and relTol_i is the relative tolerance for the same component. The user can also use only two scalar values absTol and relTol which will be used for all components.
If the Ordinary Differential Equations is an {@link ExpandableStatefulODE extended ODE} rather than a {@link org.apache.commons.math3.ode.FirstOrderDifferentialEquations basic ODE}, then only the {@link ExpandableStatefulODE#getPrimaryState() primary part}of the state vector is used for stepsize control, not the complete state vector.
If the estimated error for ym+1 is such that
sqrt((sum (errEst_i / threshold_i)^2 ) / n) < 1
(where n is the main set dimension) then the step is accepted, otherwise the step is rejected and a new attempt is made with a new stepsize.
@since 1.2