I am using euler's method to solve a differential equation, but when I run the code it doesn't plot.

Hi, I am using Euler's method to solve the differential equation dv/dt, but when I run the code it doesn't plot andI don't get an error.

Any help would be greatly appreciated. Thanks

%Eulers method

t0=0; %start time
t1= 500; %finish time
dt = 100000; %large timestep to avoid errors 
n = (t1-t0)/dt +1; %Number of nodes
t = linspace(t0,t1,n);%Time array
n_rou = round(n); %rounds n to an integer for y_euler to work
v_euler = zeros(n_rou,1); %create an empty array
v_euler(1) = 1; %initial value as v(0)=1
dvdt = @(v,t) -2.4*v(t)^2 - v(t)^3-4*v(t)+7.4 ; %anonymous function for dv/dt

for i = 1:n-1
    f = dvdt(v_euler(i),t(i)); %Evaluate f=dy/dt at i
    v_euler(i+1) = v_euler(i) + dt*f; % Evaluate y at i+1
end 

plot(t,v_euler)

Answer 1

[James Tursa]

Take a look at these lines:

t0=0; %start time
t1= 500; %finish time
dt = 100000;

Your stepsize is much larger than the total time! You need to make the stepsize reasonably small given the total time and derivative function involved.

[John D'Errico]

My guess is, @Rashmika Undu was thinking of that as the NUMBER of steps, because we see this comment:

dt = 100000; %large timestep to avoid errors 

One needs a SMALL timestep to reduce errors, and therefore many steps. Instead, had dt been a small number...

t0=0; %start time
t1= 500; %finish time
dt = 0.01; %large timestep to avoid errors 
n = (t1-t0)/dt +1

n = 50001

Now many steps, and therefore, hopefully a sufficiently small error.

[Rashmika Undu]

Yes thanks @John D'Errico, I was thinking of a large number of timesteps so the small dt makes sense.

Now when I run the code I get this error " Array indices must be positive integers or

logical values." For these two lines:

dvdt = @(v,t) -2.4*v(t)^2 - v(t)^3-4*v(t)+7.4 ; %anonymous function for dv/dt

f = dvdt(v_euler(i),t(i)); %Evaluate f=dy/dt at i

[James Tursa]

Assuming v(t) is meant to be "velocity at time t", you should just drop the (t) part since what is passed in for v is at the current time:

dvdt = @(v,t) -2.4*v^2 - v^3-4*v+7.4