Quasilinearization Approach to Nonlinear Problems in Physics

The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method could be proved are formulated and elaborated. The method, whose mathematical basis in physics was discussed recently by one of the present authors (VBM), approximates the solution of a nonlinear differential equation by treating the nonlinear terms as a perturbation about the linear ones, and unlike perturbation theories is not based on the existence of some kind of a small parameter. It is shown that the quasilinearization method gives excellent results when applied to difficult nonlinear differential equations in physics, such as the Blasius, Duffing, Lane-Emden and Thomas-Fermi equations. The first few quasilinear iterations already provide extremely accurate and numerically stable answers. PACS numbers: 02.30.Mv, 04.25.Nx, 11.15.Tk ∗Electronic mail: [email protected] †Electronic mail: [email protected]