Iterative algorithms for nonlinear ordinary differential eigenvalue problems (Q5944564)

The authors implement a Newton type algorithm, combined with the principle of argument, to compute solutions of nonlinear eigenvalue problems. The original problem is approximated by standard techniques (finite differences and, alternatively, spline collocation) to obtain a rational function, the zeros of which are the eigenvalues of interest. The calculation of the eigenfunction is more straightforward although stability considerations have also been taken care of. Numerical results for both linear and nonlinear problems illustrate the feasibility of the approach.