Question

(a) Given step size ?x = 0.25, use the Euler’s method to solve: y' = y + 2x - x², y(0) = 1, for 0 ? x ? 1 (b) Consider a cantilever beam supporting a concentrated load P at its free end. The bending of this cantilever beam is described by the differential equation: EIy'' = -P(L - x) where EI and L are the bending rigidity and the length, respectively, of the beam. Given the boundary conditions are y(0) = y'(0) = 0. Determine the deflection of the beam by using the finite difference method. In your calculation, divide the beam into 4 equal subintervals.

          (a) Given step size ?x = 0.25, use the Euler’s method to solve:
y' = y + 2x - x², y(0) = 1, for 0 ? x ? 1
(b) Consider a cantilever beam supporting a concentrated load P at its free end. The bending of this cantilever beam is described by the differential equation:
EIy'' = -P(L - x)
where EI and L are the bending rigidity and the length, respectively, of the beam. Given the boundary conditions are y(0) = y'(0) = 0.
Determine the deflection of the beam by using the finite difference method. In your calculation, divide the beam into 4 equal subintervals.

(a) Given step size ?x = 0.25, use the Euler’s method to solve:
y' = y + 2x - x², y(0) = 1, for 0 ? x ? 1
(b) Consider a cantilever beam supporting a concentrated load P at its free end. The bending of this cantilever beam is described by the differential equation:
EIy” = -P(L - x)
where EI and L are the bending rigidity and the length, respectively, of the beam. Given the boundary conditions are y(0) = y'(0) = 0.
Determine the deflection of the beam by using the finite difference method. In your calculation, divide the beam into 4 equal subintervals.

Added by Mikayla M.

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