Question

I have all of the answers to this can someone just actually explain this matlab code and the results to me so i can get a better understanding?

b)

(c) and (d)

%% Matlab code %%

clc;
close all;
clear all;
format long;
f=@(t,y)y*(1-y);
y(1)=0.01;

%%%% Exact solution
[t1 y1]=ode45(f,[0 9],y(1));
figure;
plot(t1,y1,'*');
hold on
% Eular therom
M=[32 64 128];
T=9;
fprintf(' M Max error \n' );
for n=1:length(M)
k=T/M(n);
t=0:k:T;
for h=1:length(t)-1
y(h+1)=y(h)+k*f(t(h),y(h));
end
plot(t,y);
hold on
%%% Exact solution
[t y2]=ode45(f,t,y(1));
Mer=max(abs(y2-y'));
fprintf(' %d %f \n',M(n),Mer);
end

legend('Exact solution','M=30','M=64','M=128');
xlabel('t');
ylabel('y(t)');

OUTPUT:

(a)Use Euler method to find the difference equation for the following IVP (initial value problem). Please Type your work. (Due on March 5th) dt(, yo 0.01 (b) Calculate the numerical solution for 0 s t S T using k and M T where k = and T = 9 for M 32,64, 128. Using programming languages such as Ct+, MATLAB, eto. (c) Graph those numerical solutions versus exact solution. (Due on March 19th) 32, 64, 128 where (d) Find the maximum error for each M maximum error eo naxj 1, M+1|y(5)-m y(t,) exact solution of the IVP at t - tj; y, solution of difference equation at t t, calculated by the computer. (Due on April 5th) Exact solution M-30 М-64 M-128 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 9 3 4 5 6