Abstract
A new algorithm is presented for solving nonlinear second-order coupled differential equations of the form y′ = F( x, y). Modifications of the standard Numerov procedure have resulted in a rapid, noniterative, predictor-corrector form without matrix inversion and with improved accuracy. Comparisons with the usual Numerov and de Vogelaere methods are presented for the homogeneous case F( x, y) = - G( x) y often encountered in quantum scattering theory. Tests are also presented of a version with variable step size and with stabilization by orthogonalization of the solutions at internally determined. intervals.
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