Solve using python code. Sympy, Numpy. Define a function, forward_euler, that us
ID: 3834401 • Letter: S
Question
Solve using python code. Sympy, Numpy.
Define a function, forward_euler, that uses forward Euler to solve ODEs of the form: y' + py = q and accepts the following arguments in order specified: p is the coefficient of y(x), q is right-hand side of differential equation, y is the initial value of y at t = 0 (default should be 0.0), N is the number of equally-spaced times after t = 0 to be used for the approximation (default should be 25), and t_max is the end point for approximation (default should be 10.0). The function should return y, an np. array of the approximate y(t) values, and t, an np. array of the correspond times at which y(t) is evaluated.Explanation / Answer
def ForwardEuler(f, dt, u0, T):
u=[];t=[]
#u[k]isthesolutionattimet[k] u.append(u0)
t.append(0)
n = int(round(T/dt))
for k in range(n):
unew = u[k] + dt*f(u[k], t[k])
u.append(unew)
tnew = t[-1] + dt
t.append(tnew)
return numpy.array(u), numpy.array(t)