A simple supported beam at x0 = 0 and xn = L with a uniform load w and the
vertical deflection v(x) is described by the boundary value problem
d
2
v
dx2
=
x−L
3EI
wx, v(0) = 5, v(L) = 100
where L is the length of the beam, E represents the Young’s modulus of the material from which
the beam is fabricated and I is the second moment of area of the beam’s cross–section. Suppose
L = 15 m, E = 210 kN/m
2
, I = 370.5 m2
and w = 9.8 kN/m. Use the Shooting method to
approximate the vertical deflection, v(x) with the step size, h = 3, the first guess, z0 = 10 and
the second guess, z0 = 5.
