Diferencia entre revisiones de «Usuario:Carlos Castro»
De MateWiki
| (No se muestran 3 ediciones intermedias del mismo usuario) | |||
| Línea 7: | Línea 7: | ||
: y(n+1) = y(n) + h y(n)(1 - y(n)) | : y(n+1) = y(n) + h y(n)(1 - y(n)) | ||
* MATLAB code | * MATLAB code | ||
| − | + | {{matlab|codigo= | |
| − | + | % Euler method to solve the logistic equation y'=y(1-y) | |
| − | + | clear all; | |
| − | + | t0=0; tN=4; % initial and final time | |
| − | + | y0=1/10; % value of y at time t=0 | |
| − | + | N=40; % Number of intervals | |
| − | + | h=(tN-t0)/40; % Time step h | |
| − | + | yy=y0; % yy -> variable with the solution at each time step | |
| − | + | y(1)=yy; % y -> vector where we store the solution | |
| − | + | for n=1:N-1 | |
| − | + | yy=yy+h*yy*(1-yy); % numerical scheme | |
| + | y(n+1)=yy; % store the solution | ||
| + | end | ||
| + | x=t0:h:tN; % Draw the solution | ||
| + | plot(x,y,'x'); | ||
| + | }} | ||
<gallery> | <gallery> | ||
Revisión actual del 11:31 31 ene 2013
Resolución de la Ecuación logística por el método de Euler
- Logistic equation:
- y0 = f (t, y)=y(1-y);
- y(t0) = y0:
- Numerical scheme
- y(0) = 1/10
- y(n+1) = y(n) + h y(n)(1 - y(n))
- MATLAB code
% Euler method to solve the logistic equation y'=y(1-y)
clear all;
t0=0; tN=4; % initial and final time
y0=1/10; % value of y at time t=0
N=40; % Number of intervals
h=(tN-t0)/40; % Time step h
yy=y0; % yy -> variable with the solution at each time step
y(1)=yy; % y -> vector where we store the solution
for n=1:N-1
yy=yy+h*yy*(1-yy); % numerical scheme
y(n+1)=yy; % store the solution
end
x=t0:h:tN; % Draw the solution
plot(x,y,'x');
Aproximación numérica
Error entre la solución exacta y la aproximación numérica
