The basic differential equation of the elastic curve for a simply supported, uniformly loaded beam is given as:
wLx - wX'' dx
where E is the modulus of elasticity and I is the moment of inertia. The boundary conditions are y(0) = y(L) = 0. Solve for the deflection of the beam using the finite-difference approach, specifically the shooting method with built-in functions such as 'bvp4c'.
The following parameter values apply: E = 200 (GPa), I = 30,000 (cm^4), w = 15 (kN/m), L = 3 (m), and Ax = 0.2 (m). Compare your numerical results to the analytical solution:
wLx'' - wX = wLx'' - wX