CRPC-TR91250:  Rationale for Guaranteed ODE Defect Control

Robert Coreless, George F. Corliss

December, 1991

We introduce a modification of existing algorithms that allows easier 
analysis of numerical solutions of ordinary differential equations. We 
relax the requirement that the specified problem be solved, and instead 
solve a "nearby" problem exactly, in Wilkinson's tradition of backward 
error analysis. The precise meaning of "nearby" is left to the user. This 
inexpensive algorithm sublimates the well-known difficulties associated 
with the propagation of accumulated error and avoids the difficulty of 
exponential growth of inclusion widths associated with interval 
techniques. No claim is made for the accuracy with which the specified 
problem is solved. It is shown that often no such claim is necessary.