math1902_2020

math1902_2020, MATH1902, "Directed study on numerical solution of differential equations", University of Pittsburgh, fall semester 2020, Instructor: Catalin Trenchea, Thackeray 606, Computing assistant: John Burkardt.

Location: http://people.sc.fsu.edu/~jburkardt/classes/math1902_2020/math1902_2020.html

• syllabus

Weekly assignments:

1. euler, the "humps" ODE, the forward Euler ODE solver;
   and
   euler_answers;
2. logistic, the logistic ODE; the direction field of an ODE.
   and
   logistic_answers;
3. predator, the predator/prey ODE; adjusting the Euler ODE solver to multiple ODEs; the phase plane of a pair of ODEs; the idea of conservation.
   and
   predator_answers;
4. rk, the accuracy of the Euler method, the Runge Kutta family of ODE solvers, the EXPSIN example ODE,
   and
   rk_answers;
5. error, error estimation: smaller steps or higher order;
   and
   error_answers;
6. stepsize, adjusting the stepsize to control the error, and a sneak peak at the STIFF ODE,
   and
   stepsize_answers;
7. stiff, the STIFF ODE; MATLAB's fsolve() equation solveer; implicit ODE solution methods; the QUADEX sample ODE.
   and
   stiff_answers.
8. conservation, physical laws often require certain quantities to be conserved. Some ODE solvers can enforce such a requirement.
   and
   conservation_answers.
9. midpoint, the midpoint method
   and
   midpoint_answers.
10. double_pendulum, the double pendulum ODE;