MATLAB Code for b and c

Problem 2 Consider the following boundary value problem (a) Using the second-order central difference approximation for y'", construct a tri-diagonal matrix for L[JA =-1] and solve the linear system with f(x) = x using the tri-diagonal solver introduced in class for three different values of step size h. Discuss your results in comparison with the exact solution. (b) Repeat (a) using the boundary conditions: y,(0)-0 and y(1) 0. (c) Using the shooting method discussed in class, solve the eigenvalue problem Lg; X] 0 with y(0) 0 and y(1) 0 and compute the first two eigenvalues and eigenfunctions for three different valuesofsteps zeh. Then compare the numerical solutions with the exact solutions