math2604_2021

math2604_2021, MATH 2604, "Numerical solution of time-dependent advection-diffusion-reaction equations",
University of Pittsburgh, spring semester 2021,
Instructor: Catalin Trenchea,
Computing assistant: John Burkardt.

Location: https://people.sc.fsu.edu/~jburkardt/classes/math2604_2021/math2604_2021.html

  1. advection_ftcs_pde, a MATLAB code which sets up and solves a 1D advection partial differential equation (PDE) with constant velocity and periodic boundary conditions, using the FTCS method (forward time difference, centered space difference), described in class on 29 January 2021.
  2. backward_euler, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) backward Euler method.
  3. boundary_locus, a MATLAB code plots the region of absolute stability for an ODE solution method, as described in class on 22 February 2021.
  4. burgers_pde, a MATLAB code which solves the Burgers equation for a simple model of fluid flow, as mentioned in class on 03 February 2021.
  5. diffusion_ftcs_pde, a MATLAB code which sets up and solves a 1D diffusion PDE with constant diffusion coefficient and periodic boundary conditions, using the FTCS method (forward time difference, centered space difference).
  6. euler, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (explicit) forward Euler method, described in class on 10 February 2021.
  7. gray_scott_pde, a MATLAB code which sets up and solves a system of diffusion reaction PDEs over a 2D spatial domain, using the forward Euler method for time integration, and a 9-point stencil to approximate the Laplacian, described in class on 08 February 2021.
  8. log_norm, a MATLAB code which evaluates the logarithmic norm of a matrix, for p-norm 1, 2 or oo, described in class on 15/17 February 2021.
  9. midpoint, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method.
  10. ozone2_ode, a MATLAB code which set up and solve the ozone simulation ODE, described in class on 27/29 January 2021.
  11. reaction_ode, a MATLAB code which set up and solve the reaction system of ordinary differential equations (ODE), a problem which was described in class on 22 January 2021.
  12. reaction_twoway_ode, a MATLAB code which defines the ordinary differential equations (ODE) which model a two-way chemical reaction between species W1 and W2, described in class on 12 February 2021.
  13. schroedinger_nonlinear_pde, a MATLAB code which solves the complex partial differential equation (PDE) known as Schroedinger's nonlinear equation: dudt = i uxx + gamma * |u|^2 u, in one spatial dimension, with Neumann boundary conditions.
  14. spiral_pde, a MATLAB code which solves a pair of partial differential equations (PDE) over a 2D domain with zero Neumann boundary conditions. The solution is known to form a spiral. Because of the size of the system, a simple forward Euler method is used instead of ode45().
  15. tumor_pde, a MATLAB code which solves the tumor angiogenesis partial differential equations (PDE) using MATLAB's pdepe() function.

Last revised on 22 February 2021.