Predictor-corrector formulas based on rational interpolants

AbstractTitle formulas are developed for particular use in the solution of nonlinear differential equations which in general offer no clue as to the presence of singularities on or near the path of integration. Procedure is advantageous since the approximations ascertain the existence of zeros and poles and locate these data with great accuracy. The function y = J1(x)/Jo(x) where Jn(x) is the Bessel function of the first kind satisfies a first order nonlinear differential equation of the Riccati type, and has an infinite number of zeros and poles on the positive real axis. A numerical example is provided to illustrate computation of these singular points in 0 < x < 100. Some other examples are also given

Hidden unity in nature's laws

Very detailed review of John Taylor's new introductory physics book (4 pages)