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lect11

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lect11, Wed 02/20

Ordinary differential equations (ODEs)

• Lecture Files

Reading assignment

For next week, continue reading NCM Chapter 7 through Section 7.5. Section 7.5 is about an algorithm that Matlab calls BS23 (and implements as ode23tx); this is the same algorithm that scipy calls RK23.

References for today’s lecture

NCM Sections 7.1 through 7.3 (ODEs).

Outline

• Standard form of an ODE

• Software for solving ODEs numerically
  • integrate.solve_ivp()
  • examples of first-order ODEs
  • plotting solutions to ODEs
    • plt.plot()
    • plt.legend()
    • plt.xlabel(), plt.ylabel(), plt.title()
• Systems of ODEs
  • Lotka-Volterra equations
  • phase space plots
• ODEs with higher derivatives
  • the harmonic oscillator