Problem 5 We Consider A Stiff System X 100x Y X 0 1 Y Y Y 0 1 1 A Show That The System Is Sti 1 (62.77 KiB) Viewed 30 times
1a) Should say: "Write it as a fixed point and show that it has
a unique fixed point in the interval:"
The fixed point needs to be written for the system of equations
of (x,y)
Problem 5. We consider a stiff system = x' = -100x + y, x(0) = 1 y' = - y, y(0) = 1. (1) (a) Show that the system is stiff by finding the eigenvalues of the linear map -100 1 А (2) 1 -1 Write down the solution. The solution is given by = ( = Cje-11t + Cze-12t y=Cze-lit + C4e-12t where C1, C2, C3, C4 are found from initial conditions. Here, 11 and 12 are eigenvalues of the matrix A.
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