Finite Difference Method in 1D

Consider the same equation as in Problem 1. We will now compute approximate solutions with the finite difference method.

a). Consider a uniform grid with h= (ba)/N. Set up the finite difference method for the problem. Write out this tri-diagonal system of linear equations for yi.

(b). Write a Matlab program that computes the approximate solution yi. You may either use the Matlab solver to solve the linear system, or use the code for tri-diagonal systems (you should find it in a previous homework). Test your program for N= 10 and N= 20. Plot the approximate solutions together with the exact solution. Plot also the errors.

Equation from problem 1:

Consider the differential equation

y= y+ 2y+ cos(x), for 0 x /2,

with boundary conditions: y (0) = 0.3, y(/2) = 0.1