Question: Solve y - y = 0 for the initial conditions y(0) = 1, y'(0) = -1. Then change the initial conditions to y(0) = 1.001,

Solve y" - = 0 for the initial conditions y(0) = 1, y'(0) = -1. Then change the initial conditions to y(0) = 1.001, y' (0) = -0.999 and explain why this small change of 0.001 at t = 0 causes a large change later, e.g., 22 at = 10. This is instability: a small initial difference in setting a quantity (a current, for instance) becomes larger and larger with time t. This is undesirable.

Step by Step Solution

3.48 Rating (148 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

By making the initial conditions of the system more nearly equal the current becomes less and less l... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Advanced Engineering Mathematics Questions!