All of this is just one question. Please i need help. If you can be specific on every step i would apppreciate it a lot. Thank you

Project 1: Two-Point Boundary Value Problems 1 Background Linear systems that arise in practice can become quite large in size. The purpose of this computer project is to understand why this often occurs and why there is frequently a special structure to the linear systems that come from practical applications. Given an interval a, bl and two numbers a and B, consider the general problem of trying to find a function y(t) that satisfies the differential equation u(t)y" (t) v(t)y' (t)+ w(t)y(t) f (t), with (a) a and (b) B (1) The functions tu, v, w, and f are assumed to be known functions on la bl. Because the unknown function y(t) is specified at the boundary points a and b. Equation (1) is referred to as a two-point boundary value problem. Such problems abound in nature and are frequently very hard to handle because it is often not possible to express y(t) in terms of elementary functions. Numerical methods are usually employed to approximate u(t) at discrete points inside la, bl. Approximations are produced by subdividing the interval a, bl into n 1 equal subintervals, each of length h (b-a)/(n 1) as shown in Figure 1 Derivative approximations at the interior nodes (grid points) t a tih are made by using Taylor series expansions y() 0 y ti) /k! to write ha Subtracting and adding these expressions produce y (t, h) -y (t O(ha) u'(te) (4) 2h. O(h4). (5) where O(hP) denotes terms containing pth and higher powers of h The resulting approximations h) -2y(ti) (tit and (ts) (6) h2 2h Adapted from Matrix Analysis and Applied Linear Algebra by Meyer, C.D., Society for Industrial and Applied Mathematics