rk45(ydot=[lambda x,y: y [0]],
y0=[1.0],
x0=0.0,
x1=1.0,
nx=20)
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Numerical integration of a list of ODEs using a 4th order Runge-Kutta
scheme:
h
y_{i+1} = y_i + - ( k1 + 2*k2 + 2*k3 + k4 )
6
where:
k1 = f(x_i , y_i )
k2 = f(x_i+h/2, y_i+k1*h/2)
k3 = f(x_i+h/2, y_i+k2*h/2)
k4 = f(x_i+h , y_i+k3 )
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Application Programming Interface (API):
- Parameters:
ydot ([ lambda, lambda, ... ]) - a list of ODEs provided as ydot[k] = lambda x,y:
fun_k(x,y)y0 ([ float, float, ... ]) - a list of starting values for yx0 (float) - start of integration domainx1 (float) - end of integration domainnx (int) - number of integration steps in addition to x0 - Returns: [ list, list, ... ]
- Integration history "y" defined by [ y0, y1, ... ynx ]
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