A variable interval variable step method for the solution of linear second order coupled differential equations

摘要

A new method for the numerical solution of the linear second order coupled differential equations of quantum scattering theory is presented. A formal framework is set up which makes clear the interrelationships between many currently used integration methods. Our variable interval variable step method is designed to reduce the total number of matrix (N3) operations required for solution at a given accuracy. The method is tested on several problems and is shown to be uniformly and rapidly convergent, stable, and significantly faster than previous methods.