The equations reduce to the single equation and a

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ____________________________________ page 409 —————————————————————————— CHAPTER 7. —— I A It can be shown that the partial sums on the left hand side converge for all . Taking the limit as on both sides of the equation, we obtain A Alternatively, consider the system x Ax . Since ODEs are uncoupled, the vectors x e , are a set of linearly independent solutions. Hence the matrix X e e is a fundamental matrix. Finally, since X e e I , it follows that e e 17 . Assuming that x is a solution, then both sides of the equation to obtain A. A , with A x Integrate . Hence x A . . Proceed with the iteration x With A . x , and noting that A is a constant matrix, ________________________________________________________________________ page 410 —————————————————————————— CHAPTER 7. —— x Ax x That is, I Ax A x. . We then have x AI x Ax I A Ax Ax A x. Now suppose that I A A A A A x. It follows that AI AI A A A x A A A A A x x Therefore I A By induction, the asserted form of . Define lim A A x. is valid for all . It can be shown that the...
View Full Document

This note was uploaded on 03/11/2014 for the course MA 303 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

Ask a homework question - tutors are online