Consider the following boundary value problem for u(x): {

u(x)+u'(x)+u'' (x)=f(x), x(a,b),

1u(a) + 1u(a) = 1, ₂u(b) + ₂u(b) = ₂.

Apply the second-order finite difference method to the above system. Use Use n equa-distant sub- intervals.

u = fd2_bvp(a,b,alpha,beta,gamma,alpha1,beta1,gamma1,alpha2,beta2,gamma2,f).

f is a column vector with each element as a function evaluation of f(x). u is a column vector as the numerical approximations. Use the three-point centered-difference formula for the interior points.

Use FDF2 and BDF2 formulas for the two end points.

Use the lu command to solve the linear system.

Write a "Matlab" program to do the above question. Thank you!