  In this work, we propose a numerical approach for simulations of large
deformations of interfaces in a level set framework. To obtain a fast and
viable numerical solution in both time and space, temporal discretization is
based on the composition of one-step methods exhibiting higher orders and
stability, especially in the case of stiff problems with strongly oscillatory
solutions. Numerical results are provided in the case of ordinary and partial
differential equations to show the main features and demonstrate the
performance of the method. Convergence properties and efficiency in terms of
computational cost are also investigated.
