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(Solved): (iii) Consider the stiff problem y^(')=\lambda y(t)-e^(-t)-\lambda e^(-t),t>=0 y(0)=1 whose exact ...
(iii) Consider the stiff problem
y^(')=\lambda y(t)-e^(-t)-\lambda e^(-t),t>=0
y(0)=1
whose exact solution is y(t)=e^(-t). Notice that the exact solution does not depend on the
parameter \lambda .
(a) Apply the forward Euler method to approximate the solution of the above IVP. Con-
sider the problem with \lambda =-1,-10,-50. Find an upper bound on the mesh-
size h that guarantees stability for the forward Euler method applied to each of the
three problems. 