odeEueler Explicit Eurlers method

Ok so I am working on a project and I will put the image of the problem statement and there must be somthing fundemental that I am doing incorrectly because I feel like this methodology is right for the problem

Here is my host file

%% Definining Initial Parameters for the Eueler
%yINI = [0;0]; %This describes the IC for the displacement and velocity
%h = [0.8 0.5 0.1]; %Given step sizes we will use in plots 
%te = [0 8]; % ' Time Elapsed' from 0s-->8s our x-axis

function [t,y,ydot] = odeEULER(ODE1,ODE1,a,b,h,yINI)
%a - initial value for t 
%b - last value of t 
%h - step size
%yINI - y and y dot initial values 
%Output variables- t,y,ydot
t(1) = 0; y(1) = yINI; ydot = yINI;
N= (b-a)/h;
for i=1:N
    t(i+1)=t(i) + h;
    y(i+1)=y(i) + ODE1(t(i),y(i))*h;
    ydot(i+1)=ydot(i) + ODE2(t(i),ydot(i))*h;
end

and now here is my scrpit file:

clc; clear all 
a=0;b=8;h = [0.8 0.5 0.1];yINI = [0;0];
[t,y,ydot] = odeEULER(@dydt,@dydotdt,a,b,h,yINI)

figure(1)
plot(t,y,'LineWidth',2)
xlabel('Time(s)')
ylabel('Distance travelled(m)')
title('Displacement over time')
grid on

figure(2)
plot(t,ydot,'LineWidth',2)
xlabel('Time(s)')
ylabel('Velocity (m/s)')
title('Velocity vs Time')
grid on 


function dydx=dydt(t,y,ydot)
    dydx=ydot;
end

function dydx=dydotdt(t,y,ydot)
g=32.2,w= 3000-800*t;T = 8000;D =((0.005*g)*(ydot^2));
dydx=((g/w)*(T-w-D));
end 

Please let me know what I am to

Answer 1

[Thiago Henrique Gomes Lobato]

You had many syntax errors on your code. Here is a version with them fixed and it should work. Although a negative weighting is not something that makes sense to me (it happens for t>3.75 s following your command).

clc; clear all 
a=0;b=8;h = [0.8 0.5 0.1];yINI = [0;0];

for idxH=1:3
[t,y,ydot] = odeEULER(@dydt,@dydotdt,a,b,h(idxH),yINI);
figure
plot(t,y,'LineWidth',2)
xlabel('Time(s)')
ylabel('Distance travelled(m)')
title(['Displacement over time. h = ',num2str(h(idxH))])
grid on
figure
plot(t,ydot,'LineWidth',2)
xlabel('Time(s)')
ylabel('Velocity (m/s)')
title(['Velocity vs Time. h = ',num2str(h(idxH))])
grid on 
end

function dydx=dydt(ydot)
    dydx=ydot;
end
function dydx=dydotdt(t,ydot)
g=32.2;
w= 3000-800*t;T = 8000;D =((0.005*g)*(ydot^2));
dydx=((g/w)*(T-w-D));
end 


function [t,y,ydot] = odeEULER(ODE1,ODE2,a,b,h,yINI)
%a - initial value for t 
%b - last value of t 
%h - step size
%yINI - y and y dot initial values 
%Output variables- t,y,ydot
N= (b-a)/h;
y = zeros(N,1);
ydot = zeros(N,1);
t = zeros(N,1);

t(1) = 0; y(1) = yINI(1); ydot(1) = yINI(2);
for i=1:N-1
    t(i+1)=t(i) + h;
    y(i+1)=y(i) + ODE1(ydot(i))*h;
    ydot(i+1)=ydot(i) + ODE2(t(i),ydot(i))*h;
end
end

[Yo mama]

Thank you this is helpful i see where I went wrong but the only thing Ive been trying to problem solve is how would I get the 3 different h values lines on one plot would you say. This outputs 6 graphs (3 for displacement and 3 for velocity for each 3 step sizes) How would I put those three lines in the same plot for each