# Help with Euler's Method in Matlab

1. Nov 6, 2010

### Deathcrush

1. The problem statement, all variables and given/known data
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?

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

3. 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

2. Nov 6, 2010

### viscousflow

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

3. Nov 6, 2010

### 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);

4. Nov 6, 2010

### Deathcrush

It worked!, thanks a lot