Help with Euler's Method in Matlab

[Deathcrush]

Homework Statement

Well, I'm having problems with this script, I'm taking my first course on differential equations, and I am trying to write a script that approximates the values of the solution of a differential equation, and compares them to the exact solution using a table of values, it must also calculate the error, the problem is that I cannot make the table to appear using a column for each variable, instead, the values are spread horizontally and everything is pretty messed up, Its the first time I use Matlab and I might have a lot more mistakes, can anyone help me?

Homework Equations

the equations are pretty simple, they are in the bottom of the script I wrote

The Attempt at a Solution

this is what I wrote

function [t P] = Euler(t0,P0,L,N) % Nombrando la función y estableciendo los datos necesarios

Close all;
h=L./N; % estableciendo tamaño de paso
t=[]; P=[]; % t y P son vectores vacíos
t(1)=t0+h;
P(1)=P0+h.*f(t0, P0); % Estableciendo los primeros componentes de t y P

for n=1:N-1
t(n+1)=t(n)+h;
P(n+1)=P(n)+(h.*(f(t(n), P(n))));
end

Paprox=P;
Pexacta= SolucionExacta(t);
error=abs(Pexacta-Paprox);

% Para imprimir la tabla

fprintf(' t Paproximada Pexacta error \n');
fprintf('---------------------------------------------------------------------------------\n');
fprintf( '%10.5f %10.5f %10.5f %10.5f', t ,Paprox, Pexacta, error);

% Para graficar

plot(t,P);
hold on
plot(t,Pexacta);
figure;
plot(t, error);

end
function ret=f(t,P)%para insertar la ecuación diferencial que deseamos resolver por aproximación

ret=(0.0225.*P-(0.0003.*(P.^2)));
end

function f=SolucionExacta(t) % Para establecer la solución aproximada y hacer comparación

f=(0.5625.*exp(0.0225.*t))./(0.015+(0.0075.*exp(0.0225.*t)));

end

 

[viscousflow]

The issue is you're printing arrays. You need to write your print statement in a loop, looping your values.

 

[JesseC]

As viscousflow said you'll need a for loop to print the array. Might help to add a 'next line' command into your code \n

Here:

fprintf( '%10.5f %10.5f %10.5f %10.5f \n', t ,Paprox, Pexacta, error);

 

[Deathcrush]

It worked!, thanks a lot

 

[DeeNos]

I would suggest breaking down the problem into smaller, manageable steps and checking each step along the way to ensure accuracy. Here are some potential solutions to the issues mentioned:

1. For the table of values, you can use the "fprintf" command to print the values in a specific format. For example, you can use the following code to print the values in a table with four columns:

fprintf('%10.5f %10.5f %10.5f %10.5f\n', t, Paprox, Pexacta, error);

This will print each value in a column with a width of 10 and 5 decimal places. You can adjust the format as needed.

2. It may be helpful to use a "for" loop to print each row of the table separately, rather than trying to print the entire table at once. This way, you can check each row as it is printed and make adjustments if needed.

3. Make sure to check the dimensions of your vectors "t" and "P" before printing the table. They should be the same length, and if not, you may need to adjust your code.

4. If the values are still appearing spread out horizontally, you can try transposing the vectors before printing the table. For example:

fprintf('%10.5f %10.5f %10.5f %10.5f\n', t', Paprox', Pexacta', error');

5. It may also be helpful to plot the values first to ensure they are correct before printing the table.

I hope this helps! Remember to always check your code and break down the problem into smaller steps to troubleshoot any issues. Good luck with your differential equations course!