The Quasilinearization Method (QLM) of Bellman and Kalaba for solving nonlinear differential equations has been generalized by lifting most restrictions in physical applications on the type of potentials and their ranges (V. B. Mandelzweig, J. Math. Physics 40, 6266 (1999). (See the bibliography.)

I have devised and implemented numerically the iteration scheme fot the integral-equation formulation of the QLM, which is very economical and fast, working on a fixed set of points in all iterations. An alternative differential formulation is also programmed into the code.

I calculated scattering lengths as functions of the coupling constant for several potentials, including very singular ones, in the partial wave representation giving a one-dimension problem. The bound state calculations in one dimension give 10-12 digit precision for wave functions and energies for almost any potential in a matter of seconds or minutes.

We plan to go to several dimensions soon, after streamlining the numerical implementation.

The QLM code is about 300 pages long.