CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM

                  UNIVERSITY OF COLORADO AT DENVER



TITLE:   Exponential convergence of Picard iteration for integrating 
         linear and nonlinear modally coupled equations of motion
 

SPEAKER: Joseph A. Fromme, Private Aerospace Consultant, Morrison, Colorado
         
DATE:    Monday, April 6, 1998  


PLACE:   Mathematics Conference Room 626 
         UCD Building, 1250 14th St., Denver


TIME:    noon (Refreshments served at 11:45 am) 



ABSTRACT

 An intuitive and easy to use method of Picard iteration is
shown to provide exponential computational convergence to the exact
solution of quasi-linear second order matrix differential equations with
modal coupling. Real-world applications to spacecraft structural dynamics
problems, in which the exponential convergence was first discovered, will
be discussed, as will the first mathematical proof of convergence. The
proof converts the matrix differential equation to a matrix integral
equation, uses standard functional analytic techniques to show that the
integral transformation is contracting, and applies the contraction
mapping theorem to establish uniqueness and exponential convergence. Other
applications, some quite elememtary, of Picard iteraction to solving
algebraic and integral equation will be discussed.