Naive regular perturbation

1. May 4, 2012

sam_0017

can any one hlep me with this qustion ???

Consider the equation

ε x^3 + x^2 - x - 6 = 0 ,ε > 0. (1)

1. Apply a naive regular perturbation of the form

x~$^{0}_{∞}Ʃ$ xn εn as ε→0+

do derive a three-term approximation to the solutions of (1).

2. The above perturbation expansion should only give you an approximation for 2 of the roots.
Apply a leading order balance argument to device suitable expansions for the other root, again
in the limit ε → 0+. Again, derive a three-term approximation this third case.

3. Solve (1) numerically for ε = 0.01 ?