Question

MATLAB CODE REQUIRED

Consider the problem of estimating y(0.5) for the boundary-value problem
y''+ y' = y + 2, y(0) = 0, y'(1) = 2. Find the solution using 2 approaches:

(b) Use finite difference with n = 10.Please provide Matlab code. What is y(0.5) value with Matlab?

(c) Using bvp4c. Please provide Matlab code. What is y(0.5) value with Matlab?

Answer 1

b) Using Finite Diference Method :

function output = ode45function(t,y)
   clc;
   clear all;
   close all;
   time_period = [0 10];
   intial = [0,2];
   [t,y] = ode45(@ode45function,time_period,initial);
   plot (t,y(:,1));
   figure
   plot (t,y(:,2));
output = [y(0.5); -1*y(2)+y(1)+2];

c)Using bvp4c :

function output = output_bvp(x,y)
   clc;
   clear all;
   close all;
   init = bvpinit(linespace(1,3,10),[0,2])
   sol = bvp4c(@bvp_output,init);
   x = linespace (1,3,100);
   BS=deval(sol,x);
   plot(x,BS);
output=[y(0.5); -1*y(2)+y(1)+2];