/pdf/elementary-numerical-analysis-c3jwdaojjj.pdf

Elementary Numerical Analysis

Intermediate Quantum Mechanics. By Hans A. Bethe. $9.00; paperback $4.95. 1964. (W. H. Benjamin, New York and Amsterdam)

An approximation algorithm for the solution of the nonlinear lane-emden type equations arising in astrophysics using hermite functions collocation method

Solutions of singular IVPs of Lane–Emden type by homotopy perturbation method

In this paper, approximate-exact solutions of a class of Lane–Emden type singular IVPs problems, by the variational iteration method, are presented. The variational iteration method yields solutions in the forms of convergent series with easily calculable terms. The scheme is shown to be highly accurate, and in some cases, yields exact solutions in few iterations.

Solutions of singular IVPs of Lane–Emden type by the variational iteration method

The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method of solving nonlinear ordinary differential equations could be proved are formulated and elaborated. The generalization of the proof to partial differential equations is straight forward. 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 different nonlinear ordinary 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.

V. B. Mandelzweig

Papers

Quasilinearization Approach to Nonlinear Problems in Physics with Application to Nonlinear ODEs

Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs