Knowledge Bank

A new algorithm for the numerical solution of inhomogeneous second-order differential equations is applied to the perturbation theory calculation of centrifugal distortion constants in diatomic molecules. The new scheme is similar to that of Hutson and $Howard1,2$ but entails a combined inward and outward generation of the solution, analogous to that which is used in the $Cooley3$ routine for solving the analogous homogeneous equation. The matching at an intermediate point eliminates instabilities in the nonclassical regions and permits a straightforward extraction of the desired particular solution from the initial numerical solution, which contains a component of the homogeneous solution. Numerical tests suggest that this method is capable of greater precision and efficiency than existing methods. A ``computer movie'' will be used to illustrate the method.