Plotting In MATLAB - matlab

Question

I have a code that I would like to add an additional plot inside. I want to plot the relative error of two of my functions. I am unsure where in the loop to place this so that it doesn't give me an error message and plots all three cases as single graphs. Also, my relative error code may have some mistakes, which is what may be causing the problem.
This is the relative error code:
rel_error = (y_exact1 - Y(:,2)')./y_exact; %relative error
figure()
plot(T,rel_error,'r')
This is the function I need to add it into
function ivp1()
clear;clc;close all;
t=linspace(0,2.5);
K=[.02 .1 1.5];
for i=1:3
k =K(i);
[T,Y] = ode45(#prblm1_fun,t,0); %Solving for the approximate solution to the IVP
figure()
plot(T,Y)
hold on
y_exact1 = 1/(k^2+pi^2)*(pi*exp(k*t)-pi*cos(pi*t)-k*sin(pi*t));
y_exact2 = 1/(2*k)*(exp(k*(t-1))-1) + pi/(k^2+pi^2)*(exp(k*t) + exp(k* (t-1)));
y_exact3 = 1/2/k*(exp(k*(t-1))-exp(k*(t-2))) + pi/(k^2+pi^2)*(exp(k*t) + exp(k*(t-1))) + 1/2/(k-1)*(exp(k*(t-2)) - exp(t-2));
for i=1:length(t)
if t(i)<1
plot(t(i),y_exact1(i),'mo')
hold on
elseif t(i)<2
plot(t(i),y_exact2(i),'mo')
hold on
else
plot (t(i),y_exact3(i),'mo')
hold on
end
end
end
function dy= prblm1_fun(t,y) %This is the function of the IVP for varying values of t
dy = zeros(1,1);
if t < 1
dy(1)= y(1)*k + sin(pi*t);
elseif t < 2
dy(1)= y(1)*k + 0.5;
else
dy(1)= y(1)*k + exp(t-2)/2;
end
end
end
This is the desired result for one of the k values:

Answer 1

Two erroneous places:
1) Y is a 100x1 matrix from the result of ode45. Trying to access Y(:,2) leads into a out-of-boundary error.
2) y_exact is not defined. You only have y_exact1, y_exact2 and y_exact3.
Sample code:
function ivp1()
clear;clc;close all;
t=linspace(0,2.5);
K=[.02 .1 1.5];
for i=1:3
k =K(i);
[T,Y] = ode45(#prblm1_fun,t,0); %Solving for the approximate solution to the IVP
figure()
plot(T,Y)
hold on
y_exact1 = 1/(k^2+pi^2)*(pi*exp(k*t)-pi*cos(pi*t)-k*sin(pi*t));
y_exact2 = 1/(2*k)*(exp(k*(t-1))-1) + pi/(k^2+pi^2)*(exp(k*t) + exp(k* (t-1)));
y_exact3 = 1/2/k*(exp(k*(t-1))-exp(k*(t-2))) + pi/(k^2+pi^2)*(exp(k*t) + exp(k*(t-1))) + 1/2/(k-1)*(exp(k*(t-2)) - exp(t-2));
for j=1:length(t)
if t(j)<1
y_exact = y_exact1(j);
elseif t(j)<2
y_exact = y_exact2(j);
else
y_exact = y_exact3(j);
end
plot(t(j),y_exact,'mo')
end
rel_error = (y_exact1 - Y(:,1)')./y_exact; %relative error
plot(T,rel_error,'r')
end
function dy= prblm1_fun(t,y) %This is the function of the IVP for varying values of t
dy = zeros(1,1);
if t < 1
dy(1)= y(1)*k + sin(pi*t);
elseif t < 2
dy(1)= y(1)*k + 0.5;
else
dy(1)= y(1)*k + exp(t-2)/2;
end
end
end
Sample output: