Matlab code required for 2nd order 2 point BVP

To keep things simple, consider only 2-point BVPs of the form

u′′ + q( x)u = r ( x)

subject to Dirichlet BCs u(a) = α, u(b) = β.

In order of difficulty:

Write a Matlab function with the following declaration

function u = BvpFD(q,r,a,b,alpha,beta,N)

that solves such a BVP using 2nd order central differences, constants a, b, α, β and

integer N which defines the uniform 1D mesh x1·····xN+1. Although q, r could be

function handles in simple cases, write your code so that q, r are vectors

containing the values

q ( xj ),r ( xj ), j = 1⋯N +1

This means you will have to define the mesh before you call BvpFD.