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lect16, Tue 03/03

ODEs: stiff problems

• Lecture Files

Reading assignment

Work on the sample midterm problems!

References for today’s lecture

Read NCM Section 7.9 (stiff ODEs) and this page on forward and backward Euler (you just need the methods, not the convergence analysis).

Outline

• Stiff ODEs
  • Symptoms and effects of stiffness
  • Example: the flame ODE
  • Example: the valley walk ODE
  • Motivation for implicit methods
  • The Radau implicit method (scipy demo)
  • The backward Euler method (theory)
  • Issues in implicit methods
• numpy/scipy routines
  • integrate.solve_ivp() with method=’Radau’