CS205A review_8

Scientific Computing

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: CS205 Homework #8 Review Session Notes Properties of First Order ODEs Most properties of first order scalar ODEs ( y = y ) extend naturally to their vector-valued counterparts ( y = Ay ). 1. Existence and Uniqueness . Consider the following scalar and vector-valued initial value problems: y = y, y ( t ) = y y = Ay , y ( t ) = y In both cases, a unique solution exists. 2. Well-Posedness . We say that an initial value problem is strictly well-posed if its analytic solution decays to zero as t , regardless of the initial value condition itself. For the scalar ODE y = y the necessary and sufficient condition for well- posedness is < 0. For the vector-valued case, the corresponding condition is that Re { } < 0 for any eigenvalue of A . There is also a relaxed definition for well-posedness, which is much less common. The relaxed definition requires only that the analytic solution to an initial value problem remains bounded , regardless of the initial conditions. The necessary and sufficient, regardless of the initial conditions....
View Full Document

This note was uploaded on 01/29/2008 for the course CS 205A taught by Professor Fedkiw during the Fall '07 term at Stanford.

Page1 / 2

CS205A review_8 - CS205 Homework #8 Review Session Notes...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online