fem2d_predator_prey_fast

fem2d_predator_prey_fast, an Octave code which implements finite element solvers for predator prey simulations with time and 2D spatial dependence over an arbitrary domain that has been triangulated. A variety of boundary conditions may be specified. The solvers integrate the associated partial differential equations (PDE) over a given time interval, and create plots of the predator and prey population densities at the final time.

These codes are a finite element generalization of earlier algorithms developed using the finite difference method.

The algorithms presented here are fast versions of scripts that were originally written by Marcus Garvie, of the University of Guelph. They have been modified by John Burkardt to run much more quickly.

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Languages:

fem2d_predator_prey_fast is available in a MATLAB version and an Octave version.

Related Data and Programs:

fem2d_predator_prey_fast_test

fd_predator_prey, an Octave code which solves a pair of predator prey ODE's using a finite difference approximation.

fd1d_predator_prey, an Octave code which uses finite differences to solve a 1D predator prey problem.

fd2d_predator_prey, an Octave code which implements a finite difference algorithm for a predator-prey system with spatial variation in 2D.

Author:

Original MATLAB versions by Marcus Garvie; Modifications by John Burkardt.

Reference:

1. https://www.uoguelph.ca/~mgarvie/ , Marcus Garvie's web page.
2. Marcus Garvie, John Burkardt, Jeff Morgan,
   Simple finite element methods for approximating predator-prey dynamics in two dimensions using Matlab,
   Submitted to Bulletin of Mathematical Biology.
3. Marcus Garvie,
   Finite-Difference Schemes for Reaction-Diffusion Equations Modeling Predator-Prey Interactions in MATLAB,
   Bulletin of Mathematical Biology,
   Volume 69, Number 3, 2007, pages 931-956.

Source Codes:

fe2d_D: Scheme 2 applied to Kinetics 1 with pure Dirichlet boundary conditions. This problem is posed on a region whose nodes and triangulation are supplied by the user. The sample problem uses the lake.

• fe2d_d_fast.m

fe2d_N: Scheme 2 applied to Kinetics 1 with pure Neumann boundary conditions. This problem is posed on a region whose nodes and triangulation are supplied by the user. The sample problem uses the lake.

• fe2d_n_fast.m

fe2d_ND: Scheme 2 applied to Kinetics 1 with a mixture of Neumann and Dirichlet boundary conditions. This problem is posed on a region whose nodes and triangulation are supplied by the user. The user must also supply lists of the boundary nodes at which Neumann and Dirichlet conditions are to be applied. The sample problem uses the lake.

• fe2d_nd_fast.m

fe2d_NR: Scheme 2 applied to Kinetics 1 with a mixture of Neumann and Robin boundary conditions. This problem is posed on a region whose nodes and triangulation are supplied by the user. The user must also supply lists of the boundary nodes at which Neumann and Robin conditions are to be applied. The sample problem uses the lake.

• fe2d_nr_fast.m

fe2d_P: Scheme 2 applied to Kinetics 1 with periodic boundary conditions. This problem is posed on the unit square.

• fe2d_p_fast.m

fe2d_R: Scheme 2 applied to Kinetics 1 with pure Robin boundary conditions. This problem is posed on a region whose nodes and triangulation are supplied by the user. The sample problem uses the lake.

• fe2d_r_fast.m

fe2dX_D: Scheme 1 applied to Kinetics 1 with pure Dirichlet boundary conditions. This problem is posed on a region whose nodes and triangulation are supplied by the user. The sample problem uses the lake.

• fe2dx_d_fast.m

fe2dX_N: Scheme 1 applied to Kinetics 1 with pure Neumann boundary conditions. This problem is posed on a region whose nodes and triangulation are supplied by the user. The sample problem uses the lake.

• fe2dx_n_fast.m

fe2dX_ND: Scheme 1 applied to Kinetics 1 with a mixture of Neumann and Dirichlet boundary conditions. This problem is posed on a region whose nodes and triangulation are supplied by the user. The user must also supply lists of the boundary nodes at which Neumann and Dirichlet conditions are to be applied. The sample problem uses the lake.

• fe2dx_nd_fast.m

fe2dX_NR: Scheme 1 applied to Kinetics 1 with a mixture of Neumann and Robin boundary conditions. This problem is posed on a region whose nodes and triangulation are supplied by the user. The user must also supply lists of the boundary nodes at which Neumann and Robin conditions are to be applied. The sample problem uses the lake.

• fe2dx_nr_fast.m

fe2dX_NR_ALT: Scheme 1 applied to Kinetics 1 with a mixture of Neumann and Robin boundary conditions. This problem is posed on a region whose nodes and triangulation are supplied by the user. The user must also supply lists of the boundary nodes at which Neumann and Robin conditions are to be applied. This program is the same as that in fe2dX_NR, except that the Robin condition is applied implicitly. The sample problem uses the lake.

• fe2dx_nr_alt_fast.m

fe2dX_P: Scheme 1 applied to Kinetics 1 with periodic boundary conditions. This problem is posed on the unit square.

• fe2dx_p_fast.m

fe2dX_R: Scheme 1 applied to Kinetics 1 with pure Robin boundary conditions. This problem is posed on a region whose nodes and triangulation are supplied by the user. The sample problem uses the lake.

• fe2dx_r_fast.m

Auxilliary functions include:

• boundedges.m, finds all the boundary edges in a triangular mesh.
• gauss_seidel.m, uses the Gauss-Seidel iteration to seek a solution of a linear system.
• jacobi.m, uses the Jacobi iteration to seek a solution of a linear system.
• mesh2d_example.m, code which describes points that outline the lake region, and calls mesh2d to fill the interior of the region with a grid of nodes, and to compute a triangulation of these nodes.
• subsetconnectivity.m finds the boundary edges in a triangular mesh for a portion of the boundary.