Diferencia entre revisiones de «Logistic equation»
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| Línea 9: | Línea 9: | ||
== Numerical scheme == | == Numerical scheme == | ||
| − | + | We propose an Euler explicit method, | |
| − | <math> | + | <math> y_0 = 1/10</math> |
| + | |||
| + | <math>y_{n+1} = y_{n} + h\cdot y_{n}\cdot(1 - y_{n})</math> | ||
== MATLAB code == | == MATLAB code == | ||
Revisión del 15:55 31 ene 2013
Este artículo explica la resolución de la Ecuación logística por el método de Euler.
1 Logistic equation
[math]y_0 = f(t,y) = y\cdot (1-y)[/math]
[math]y(t_0) = y_0[/math]
2 Numerical scheme
We propose an Euler explicit method,
[math] y_0 = 1/10[/math]
[math]y_{n+1} = y_{n} + h\cdot y_{n}\cdot(1 - y_{n})[/math]
3 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');
