The Wronskian of discrete methods in linear systems

Summary

In the past decade it has been suggested that the use of superposition of particular solutions technique may be employed to solve linear systems with considerable programming advantage over the more widely used method of superposition of homogeneous and particular solutions, when solving numerically multi-point boundary-value problems. The present article on analytical expression for the discretization errors of the Wronskian, induced by the discretization errors of the particular solutions, is found for linear systems of ordinary differential equations when single-step methods of numerical integration of the Runge-Kutta type are used. It is shown that the analysis of this error can, in some cases, give useful information in the estimation of optimum integration step size in the sense that minimum errors, discretization plus round-off, are attained during integration.