Economics Dynamics Problems 200

Economics Dynamics Problems 200 - Example 4.18 Consider...

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

View Full Document Right Arrow Icon
184 Economic Dynamics Figure 4.32. The procedure generalises quite readily to systems of equations. Let dx dt = f ( x , y ) dy dt = g ( x , y ) (4.32) denote a system of autonomous differential equations and let the initial value of the system be x ( t 0 ) = x 0 and y ( t 0 ) = y 0 . Then x 1 = x 0 + f ( x 0 , y 0 ) ± t y 1 = y 0 + g ( x 0 , y 0 ) ± t (4.33) which can be repeated for further (approximate) values on the solution curve. For an autonomous system in which y = φ ( x ), then such a procedure allows us to plot the trajectory in the phase plane.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Example 4.18 Consider example 4.6 given by the differential equations: dx dt = f ( x , y ) = − 2 x − y + 9 dy dt = g ( x , y ) = − y + x + 3 with x ( t ) = 2 and y ( t ) = 2. Given these values, and letting ± t = . 01, then f ( x , y ) = − 2(2) − 2 + 9 = 3 g ( x , y ) = − 2 + 2 + 3 = 3...
View Full Document

This note was uploaded on 12/14/2011 for the course ECO 3023 taught by Professor Dr.gwartney during the Fall '11 term at FSU.

Ask a homework question - tutors are online