Quasilinearization method and its application to physical problems

The general properties of quasilinearization method (QLM), particularly its fast quadratic convergence, monotonicity and numerical stability are analyzed and illustrated on different physical problems. The method, whose mathematical basis in physics was discussed recently by the present author approaches the solution of a nonlinear differential equation by approximating the nonlinear terms by a sequence of the linear ones, and is not based on the existence of some kind of a small parameter, which enables the summation of many orders of the perturbation theory as well of the 1/N expansion series.