Euler.sagews

### Metodo de Euler
def Euler(fun, a, b, N, y0):
    h = (b - a)/N
    x = [a]
    y = [y0]
    
    for k in range(N):
        x.append(x[k]+h)
        y.append(y[k]+(h)*fun(x[k], y[k]))
        
    return zip(x, y)
    
##### Datos iniciales
x = var('x') 
y = var('y')
f(x,y) = 2*x - 3*y + 1              ## -> cambiar aquí la función f(x, y)
y0=5                                ## Valor inicial en 'y'                                
a = 1.0                             ## Extremo inferior sobre 'x'
b = 1.2                             ## Extremo superior sobre 'x'


##### Solución numérica para h=0.1
n = 2                              ## numero de pasos a modificar para ver aproximación
Euler_puntos=Euler(f, a, b, n, y0)
print 'Tabla para valores de h=0.1'
print table(Euler_puntos, header_row=["x", "y"], frame='true', align='center')
p0=line(Euler_puntos,color=(1,0,1), legend_label='$y\'(x)= 2x - 3y + 1$',gridlines=True)
show(p0,axes_labels=([r'$x$',r'$y = f(x)$']))

##### Solución numérica para h=0.05
n = 4                              ## numero de pasos a modificar para ver aproximación
Euler_puntos=Euler(f, a, b, n, y0)
print 'Tabla para valores de h=0.05'
print table(Euler_puntos, header_row=["x", "y"], frame='true', align='center')
p0=line(Euler_puntos,color=(1,0,1), legend_label='$y\'(x)= 2x - 3y +1$',gridlines=True)
show(p0,axes_labels=([r'$x$',r'$y = f(x)$']))

Tabla para valores de h=0.1 +------------------+------------------+ | x | y | +==================+==================+ | 1.00000000000000 | 5 | +------------------+------------------+ | 1.10000000000000 | 3.80000000000000 | +------------------+------------------+ | 1.20000000000000 | 2.98000000000000 | +------------------+------------------+

Tabla para valores de h=0.05 +------------------+------------------+ | x | y | +==================+==================+ | 1.00000000000000 | 5 | +------------------+------------------+ | 1.05000000000000 | 4.40000000000000 | +------------------+------------------+ | 1.10000000000000 | 3.89500000000000 | +------------------+------------------+ | 1.15000000000000 | 3.47075000000000 | +------------------+------------------+ | 1.20000000000000 | 3.11513750000000 | +------------------+------------------+