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Analysis of yet another method for solving ODEs In case you haven't realized, there are a lot of methods for solving ODEs, with various properties. This homework set asks you to analyze one of them to determine its order of accuracy and stability characteristics. Here's the method: In [16]: def unknownMethod (f,ye,t): npts = t.shape[0] y = np.zeros((npts, yo.shape[0])) y[0] = ye for i in range(0,npts-1): h = t[i+1]-t[i] k1 = f(y[i], t[i]) k2 = f(y[i]+2.0hk1/3.0,t[i]+2.0h/3.0) y[i+1] = y[i] + h(0.25k1 + 0.75k2) return y This method is one of a class of very commonly-used ODE solvers called Runge-Kutta methods. question 1 Define a function describing the system of ordinary differential equations With $k/m = 1 \text{ s}^{-2}$. (I.e. the mass-spring oscillator described in lecture) $\frac{dx}{dt} = v$ $\frac{dv}{dt} = -\frac{k}{m}x$

          Analysis of yet another method for solving ODEs
In case you haven't realized, there are a lot of methods for solving ODEs, with various properties. This homework set asks you to analyze one of them to
determine its order of accuracy and stability characteristics.
Here's the method:
In [16]: def unknownMethod (f,ye,t):
npts = t.shape[0]
y = np.zeros((npts, yo.shape[0]))
y[0] = ye
for i in range(0,npts-1):
h = t[i+1]-t[i]
k1 = f(y[i], t[i])
k2 = f(y[i]+2.0*h*k1/3.0,t[i]+2.0*h/3.0)
y[i+1] = y[i] + h*(0.25*k1 + 0.75*k2)
return y
This method is one of a class of very commonly-used ODE solvers called Runge-Kutta methods.
question 1
Define a function describing the system of ordinary differential equations
With $k/m = 1 \text{ s}^{-2}$.
(I.e. the mass-spring oscillator described in lecture)
$\frac{dx}{dt} = v$
$\frac{dv}{dt} = -\frac{k}{m}x$

Analysis of yet another method for solving ODEs
In case you haven't realized, there are a lot of methods for solving ODEs, with various properties. This homework set asks you to analyze one of them to
determine its order of accuracy and stability characteristics.
Here's the method:
In [16]: def unknownMethod (f,ye,t):
npts = t.shape[0]
y = np.zeros((npts, yo.shape[0]))
y[0] = ye
for i in range(0,npts-1):
h = t[i+1]-t[i]
k1 = f(y[i], t[i])
k2 = f(y[i]+2.0*h*k1/3.0,t[i]+2.0*h/3.0)
y[i+1] = y[i] + h*(0.25*k1 + 0.75*k2)
return y
This method is one of a class of very commonly-used ODE solvers called Runge-Kutta methods.
question 1
Define a function describing the system of ordinary differential equations
With k/m = 1 s^-2.
(I.e. the mass-spring oscillator described in lecture)
(dx)/(dt) = v
(dv)/(dt) = -(k)/(m)x

Added by Brooke W.

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