  The problem of hydraulic fracture propagation is considered by using its
recently suggested modified formulation in terms of the particle velocity, the
opening in the proper degree, appropriate spatial coordinates and
$\varepsilon$-regularization. We show that the formulation may serve for
significant increasing the efficiency of numerical tracing the fracture
propagation. Its advantages are illustrated by re-visiting the Nordgren
problem. It is shown that the modified formulation facilitates (i) possibility
to have various stiffness of differential equations resulting after spatial
discretization, (ii) obtaining highly accurate and stable numerical results
with moderate computational effort, and (iii) sensitivity analysis. The
exposition is extensively illustrated by numerical examples.
