Suppose that the maximum eigenvalue (in modulus) of the Jacobian matrix associated with the right side of the system of differential equations evaluated at the initial values is l_max. In the case that the selected numerical method is not A₀-stable, in the method properties panel we have an upper limit for |hl_max|. Let this limit be L. In EpODE, the maximum stepsize in which the condition of stability is fulfilled is considered to be L/|l_max|. In the case that the selected method is A₀-stable, in the method properties panel we have the message 'Unbounded' region of stability. In this case, the stepsize is not restricted by the stability condition. In the corresponding field (for the maximum value of the stepsize) we get the message 'Unbounded'.

There are many formulae for the global error estimation which depend on the selected formula. We must adopt here a general schema for estimate the global error. In the actual implementation, the maximum limit of the stepsize due to the accuracy condition is the following:

where l_max is the above described eigenvalue, p is the method order reported by EpODE in the method properties panel, c^* is error constant of the method, reported in the same panel, and T is the length of the integration interval. This formula is valid only for this version of EpODE. In the next version we hope to find a more correct estimation. Numerical tests have been shown that the above estimation of the stepsize can give the expected results for a large variety of problems and methods.

Example for the method DIRK4 applied to the system B1.