Problem $2(4\backslash$times $10$ pts$)$

Solve for the axial displacements for the non$-$prismatic bar shown above using $($a$)$ collocation, $($b$)$ sub$-$domain, $($c$)$ least squares and $($d$)$ Galerkin's method. Assume: $E={10}^7,L=20in,,A_0=2i{n}^2$ and $P=1000lb.$ Choose a cubic trial function, $u(x)=c_1{x}^3+c_2{x}^2+c_{3}x.$ Compare with exact solution given below:

Exact solution