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Tolerance update in exercise
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ODES2_spectral.ipynb

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"which corresponds to a simple harmonic oscillator with constant frequency $\\omega = 100$.\n",
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"\n",
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"* a) First, write a function `f_ivp(t, u)` that encodes this ODE as a system of first-order ODEs and returns the derivative of the vector of unknowns, `u`. It need not have a detailed docstring.\n",
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"* b) Then define the initial conditions and solution interval. Call `scipy.integrate.solve_ivp` or a similar method (that uses a default Runge--Kutta) to solve the IVP to about 12 digits of accuracy. Think about whether it makes sense to set a relative tolerance, an absolute tolerance, or both. \n",
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"* b) Then define the initial conditions and solution interval. Call `scipy.integrate.solve_ivp` or a similar method (that uses a default Runge--Kutta) to solve the IVP to about **6** digits of accuracy. Think about whether it makes sense to set a relative tolerance, an absolute tolerance, or both. \n",
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"* c) Time the solution and print the result.\n",
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"Now we'll solve the IVP with a spectral method. \n",

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