Compare the accuracy and the range of validity of both approximate solutions.
A vibrating system is governed by the differential equationd2udt2−(u2dudt+u)+ 4u= 0, u(0) = 0,dudt(0) =v,0< 1,wherev >0is a constant parameter. 1) Determine the first two non-zero terms in the regular perturbation expansion foruas→0, and state whether the expansion is uniform int.[20 marks] 2) By introducing the two timescales,T0=tandT1=tobtain the leading-order term inthe expansion ofuas→0, which […]