Approximation of Poles and Branch Points of Solutions to Certain Nonlinear Differential Equations using Modified Piecewise Pade Approximations

摘要

A simple method is presented to numerically approximate the location of poles and branch point singularities of solutions to certain nonlinear differential equations. The general method uses a modified piecewise-Pade type of approximation. The formulas greatly simplify in the case of second order nonlinear differential equations. Several numerical examples are presented which demonstrate the ease of implementation and efficiency of the methods.