2.1) Consider the initial value problem
Find a two-term perturbation approximation u=u(t) for
2.2) Verify the following order relations:
a)
b)
c)
d)
2.3) Use Poincaré-Lindstedt’s method to get a two-term perturbation approximation y=y(t) to the problem
2.4) Consider the initial value problem
Use regular perturbation methods to achieve a three-term approximate solution y=y(t) for t>0.
2.5) Show that regular perturbation fails for the boundary value problem
Find the exact solution y=y(t). If
show that
is large. If
show that
Find the inner and outer approxiamtions from the exact solution.
2.6) Suppose that
and use singular perturbation to find an approximate solution y=y(t) to the problem
2.7) Show why singular perturbation fails for the boundary value problem
by comparing with the exact solution y=y(t).
2.8) Try singular perturbation on the boundary value problem
Discuss the result.