Question

Using hand work for the parts with a paper next to them, and MatLab for the parts with the MatLab logo next to them, complete the following:

Consider the linear BVP 4y " + 3y , + y = 0, 0<x<1 y(0)1 You will define a set of linear equations for yi,0, (yi y(Xi), 1 = o,.. . ,n) and the set of nodes is with xi-ih, 1-0, . . . , n and h =-. n is a fixed positive integer. (a) Write the forward difference approximation for y, on the nodes. Use the approximations y's Include the relevant set of i values for which the approximation holds (b) Write the centered difference approximation for y" on the nodes. Use the approximations yi's Include the relevant set of i values for which the approximation holds. (c) Write the linear equations you will need to solve for the yi's. Include the relevant set of i values. (d) Based on the previous part, write a linear system in matrix form for the approximations yi's, considering the boundary conditions as wel (e)Sove the linear system in the previous part with h 0.01 using the backslash operator. Store the approximations in a vector y. The matrix of the system at this step should be tridiagonal. Notice that the first and last elements in y can be obtained just by the boundary conditions 4A (f) Plot the approximate solution versus x, using the nodes and your vector y.

Answer 1

Limn k n h