- allen_cahn_pde, an Octave code which sets up and solves the Allen-Cahn reaction-diffusion partial differential equation (PDE) in 1 space dimension and time.
- allen_cahn_pde_test
- arenstorf_ode, an Octave code which sets up and solves an ordinary differential equation (ODE) which defines a stable periodic orbit of a spacecraft around the Earth and the Moon.
- arenstorf_ode_test
- axon_ode, an Octave code which sets up and solves the ordinary differential equations (ODE) for the Hodgkin-Huxley model of an axon.
- axon_ode_test
- backward_euler, an Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) backward Euler method, using fsolve() for the implicit equation.
- backward_euler_test
- backward_euler_fixed, an Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) backward Euler method, using a fixed point iteration for the implicit equation.
- backward_euler_fixed_test
- biochemical_linear_ode, an Octave code which sets up and solves a linear biochemical ordinary differential equation (ODE).
- biochemical_linear_ode_test
- biochemical_nonlinear_ode, an Octave code which sets up and solves a nonlinear biochemical ordinary differential equation (ODE).
- biochemical_nonlinear_ode_test
- blowup_ode, an Octave code which sets up and solves an ordinary differential equation (ODE) y'=y^2. whose solution "blows up" in finite time.
- blowup_ode_test
- boundary_word, an Octave code which works with a polyomino that is described by its boundary word, a sequence of U/D/L/R symbols that indicate how to trace out its boundary.
- boundary_word_test
- box_games, an Octave code which assists in the display of game boards (checkers, cellular automatons, life);
- box_games_test
- brusselator_ode, an Octave code which sets up and solves the Brusselator ordinary differential equation (ODE) system.
- brusselator_ode_test
- chrpak, an Octave code which manipulates characters and strings;
- chrpak_test
- conservation_ode, an Octave code which monitors the conservation of a quantity that should be constant, during the solution of an ordinary differential equation (ODE).
- conservation_ode_test
- diophantine_nd, an Octave code which is given a Diophantine equation in N variables, and returns all nonnegative solutions, or all strictly positive solutions.
- diophantine_nd_test
- dosage_ode, an Octave code which sets up and solves a system of ordinary differential equations (ODE) to simulate the blood levels of a medicinal drug that should stay between medicinal and toxic limits.
- dosage_ode_test
- double_well_ode, an Octave code which sets up and solves an ordinary differential equation (ODE) which models the motion of a particle in a double well potential.
- double_well_ode_test
- duffing_ode, an Octave code which sets up and solves a second-order ordinary differential equation (ODE) whose solution can exhibit chaotic behavior.
- duffing_ode_test
- eternity, an Octave code which considers the eternity puzzle, an irregular dodecagon that is to be tiled by 209 pieces, each formed by 12 contiguous 30-60-90 triangles, known as polydrafters.
- eternity_test
- eternity_tile, an Octave code which considers the individual tiles of the eternity puzzle, 209 distinct pieces, each formed by 36 contiguous 30-60-90 triangles, known as polydrafters.
- eternity_tile_test
- euler, an Octave code which solves one or more ordinary differential equations (ODE) using the forward Euler method.
- euler_test
- exp_ode, an Octave code which sets up and solves an ordinary differential equation (ODE) whose solution is an exponential function.
- exp_ode_test
- fitzhugh_nagumo_ode, an Octave code which sets up and solves the Fitzhugh-Nagumo system of ordinary differential equations (ODE).
- fitzhugh_nagumo_ode_test
- flame_ode, an Octave code which sets up and solves an ordinary differential equation (ODE) which models the growth of a ball of flame in a combustion process.
- flame_ode_test
- fsolve_test, an Octave code which calls fsolve() which seeks the solution x of one or more nonlinear equations f(x)=0.
- glomin, an Octave code which finds a global minimum of a scalar function of a scalar variable, without the use of derivative information, by Richard Brent.
- glomin_test
- graphics_test, Octave codes which graphically display various kinds of data.
- grazing_ode, an Octave code which sets up and solves a pair of ordinary differential equations (ODE) that model the populations of an edible plant, and the herbivore that grazes on it.
- grazing_ode_test
- hello, an Octave code which prints out "Hello, world!".
- hello_test
- henon_heiles_ode, an Octave code which sets up and solves the Henon-Heiles system of ordinary differential equations (ODE) which model the motion of a star around the galactic center.
- henon_heiles_ode_test
- humps_ode, an Octave code which sets up and solves an ordinary differential equation (ODE) whose solution is a double hump curve.
- humps_ode_test
- i4lib, an Octave code which contains many utility routines, using single precision integer (I4) arithmetic.
- i4lib_test
- kepler_ode, an Octave code which sets up and solves the ordinary differential equations (ODE) for a Kepler two-body gravitational system.
- kepler_ode_test
- kepler_perturbed_ode, an Octave code which sets up and solves the ordinary differential equations (ODE) for a perturbed Kepler two-body gravitational system.
- kepler_perturbed_ode_test
- local_min, an Octave code which finds a local minimum of a scalar function of a scalar variable, without the use of derivative information, by Richard Brent.
- local_min_test
- local_min_rc, an Octave code which finds a local minimum of a scalar function of a scalar variable, without the use of derivative information, using reverse communication (RC), by Richard Brent.
- local_min_rc_test
- lorenz_ode, an Octave code which sets up and solves the Lorenz system of ordinary differential equations (ODE).
- lorenz_ode_test
- midpoint, an Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method.
- midpoint_test
- midpoint_explicit, an Octave code which solves one or more ordinary differential equations (ODE) using the (explicit) midpoint method, also called the modified Euler method.
- midpoint_explicit_test
- midpoint_fixed, an Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, using a simple fixed-point iteration to solve the implicit equation.
- midpoint_fixed_test
- navier_stokes_2d_exact, an Octave code which evaluates an exact solution to the incompressible time-dependent Navier-Stokes equations (NSE) over an arbitrary domain in 2D.
- navier_stokes_2d_exact_test
- normal_ode, an Octave code which sets up and solves an ordinary differential equation (ODE) defining the normal probability density function (PDF).
- normal_ode_test
- octopus, a Octave code which contains some Octave-specific utilities.
- octopus_test
- oregonator_ode, an Octave code which sets up and solves the ordinary differential equations (ODE) that define the Oregonator, a model of the Belousov-Zhabotinsky chemical reaction.
- oregonator_ode_test
- oscillator_ode, an Octave code which sets up and solves the highly oscillatory ordinary differential equation (ODE).
- oscillator_ode_test
- ozone_ode, an Octave code which sets up and solves a stiff system of four ordinary differential equations (ODE) that simulate the daily variation in atmospheric ozone concentration.
- ozone_ode_test
- ozone2_ode, an Octave code which sets up and solves a stiff system of four ordinary differential equations (ODE) that simulate the daily variation in atmospheric ozone concentration. This version of the ozone ODE includes a nitrogen oxide source term.
- ozone2_ode_test
- pariomino, an Octave code which considers pariominoes, which are polyominoes with a checkerboard parity.
- pariomino_test
- pendulum_double_ode, an Octave code which sets up and solves the double pendulum ordinary differential equation (ODE).
- pendulum_double_ode_test
- pendulum_elastic_ode an Octave code which sets up and solves the ordinary differential equations (ODE) that represent the behavior of a nonlinear elastic pendulum, with gravitational force G, spring constant K, unstretched length L, and mass M.
- pendulum_elastic_ode_test
- pendulum_nonlinear_ode, an Octave code which sets up and solves the ordinary differential equations (ODE) that represent a nonlinear model of the behavior of a pendulum of length L under a gravitational force of strength G.
- pendulum_nonlinear_ode_test
- pendulum_ode, an Octave code which sets up and solves the ordinary differential equations (ODE) that represent a linear model of the behavior of a pendulum of length L under a gravitational force of strength G.
- pendulum_ode_test
- persistence, an Octave code which demonstrates how to initialize, get, or set data stored within a function, using static/persistent/saved/local memory.
- persistence_test
- polar_ode, an Octave code which sets up and solves an ordinary differential equation (ODE) whose variable is complex, and whose solution should be viewed in a polar coordinate plot.
- polar_ode_test
- polpak, an Octave code which evaluates a variety of mathematical functions, including Chebyshev, Gegenbauer, Hermite, Jacobi, Laguerre, Legendre polynomials, and the Collatz sequence.
- polpak_test
- polyiamonds, an Octave code which works with polyiamonds, simple shapes constructed by edgewise connections of congruent equilateral triangles.
- polyiamonds_test
- polyomino_parity, an Octave code which uses parity considerations to determine whether a given set of polyominoes can tile a specified region.
- polyomino_parity_test
- polyominoes, an Octave code which defines, solves, and plots a variety of polyomino tiling problems, which are solved by a direct algebraic approach, instead of the more typical brute-force or backtracking methods.
- polyominoes_test
- predator_prey_ode, an Octave code which sets up and solves a time-dependent predator-prey system of ordinary differential equations (ODE).
- predator_prey_ode_test
- quadex_ode an Octave code which sets up and solves a stiff ordinary differential equation (ODE), whose exact solution is a parabola, but for which errors grow exponentially.
- quadex_ode_test
- quasiperiodic_ode, an Octave code which sets up and solves a system of ordinary differential equations (ODE) for a problem with a quasiperiodic solution.
- quasiperiodic_ode_test
- r8lib, an Octave code which contains many utility routines, using double precision real (R8) arithmetic.
- r8lib_test
- reaction_ode, an Octave code which sets up and solves the ordinary differential equations (ODE) which model a simple chemical reaction A+B --k--> C.
- reaction_ode_test
- reaction_twoway_ode, an Octave code which sets up and solves the ordinary differential equations (ODE) which model a two-way chemical reaction between species W1 and W2.
- reaction_twoway_ode_test
- rigid_body_ode, an Octave code which sets up and solves the ordinary differential equations (ODE) representing the Euler equations for a rigid body with three unequal moments of inertia, originally proposed by Fred Krogh.
- rigid_body_ode_test
- ripple_ode, an Octave code which sets up and solves an ordinary differential equation (ODE) whose solutions start as ripples and end as hyperbolas.
- ripple_ode_test
- rk12, an Octave code which applies Runge-Kutta (RK) solvers of order 1 and 2 to a system of ordinary differential equations (ODE);
- rk12_test
- rk23, an Octave code which applies Runge-Kutta (RK) solvers of order 2 and 3 to a system of ordinary differential equations (ODE);
- rk23_test
- rk34, an Octave code which applies Runge-Kutta (RK) solvers of order 3 and 4 to a system of ordinary differential equations (ODE);
- rk34_test
- rk4, an Octave code which applies the fourth order Runge-Kutta (RK) algorithm to estimate the solution of an ordinary differential equation (ODE) at the next time step.
- rk4_test
- rk45, an Octave code which applies Runge-Kutta (RK) solvers of order 4 and 5 to a system of ordinary differential equations (ODE);
- rk45_test
- rkf45, an Octave code which applies a Runge-Kutta-Fehlberg (RKF) solver to a system of ordinary differential equations (ODE);
- rkf45_test
- robertson_ode, an Octave code which sets up and solves a system of three nonlinear stiff ordinary differential equations (ODE) characterizing an autocatalytic chemical reaction.
- robertson_ode_test
- roessler_ode, an Octave code which sets up and solves the 3D Roessler system of ordinary differential equations (ODE).
- roessler_ode_test
- rubber_band_ode, an Octave code which sets up and solves a set of ordinary differential equations (ODE) describing a mass suspended by a spring and rubber band, which can exhibit chaotic behavior.
- rubber_band_ode_test
- sawtooth_ode, an Octave code which sets up and solves an ordinary differential equation (ODE) driven by a right hand side which is a sawtooth function (periodic, discontinuous, piecewise linear).
- sawtooth_ode_test
- sir_ode, an Octave code which sets up and solves the ordinary differential equations (ODE) which simulate the spread of a disease using the Susceptible/Infected/Recovered (SIR) model.
- sir_ode_test
- sling_ode, an Octave code which sets up and solves a system of ordinary differential equations (ODE) for which the exact circular solution can only be approximated for a short interval before it decays to zero.
- sling_ode_test
- spring_ode, an Octave code which sets up and solves a system of ordinary differential equations (ODE) for the motion of a spring with mass m, damping b, and stiffness k.
- spring_ode_test
- spring_double_ode, an Octave code which sets up and solves a system of ordinary differential equations (ODE) for a system in which a mass is connected by a spring to a mass connected by a spring to a fixed support.
- spring_double_ode_test
- spring_sweep_ode, an Octave code which computes a grid of solutions to a parameterized system of ordinary differential equations (ODE) that represent the motion of a spring with mass m, damping b, and stiffness k.
- spring_sweep_ode_test
- squircle_ode, an Octave code which sets up and solves a system of ordinary differential equations (ODE) for a pair of functions that generalize the sine and cosine, and whose phase portrait is a squircle, a sort of squared circle.
- squircle_ode_test
- stetter_ode, an Octave code which sets up and solves an ordinary differential equation (ODE) for which a specific time step sequence causes the implicit trapezoidal method to be unstable, while the implicit midpoint method will be stable. Note that the right hand side function f(t,y) is periodic, discontinuous, and piecewise linear.
- stetter_ode_test
- stiff_ode, an Octave code which sets up and solves an ordinary differential equation (ODE) which is an example of a stiff ODE.
- stiff_ode_test
- string_pde, an Octave code which sets up and solves the partial differential equations (PDE) describing a vibrating string, creating files that can be displayed by gnuplot().
- string_pde_test
- subset, an Octave code which enumerates, generates, randomizes, ranks and unranks combinatorial objects including combinations, compositions, Gray codes, index sets, partitions, permutations, polynomials, subsets, and Young tables. Backtracking routines are included to solve some combinatorial problems.
- subset_test
- test_mat, an Octave code which defines test matrices for which the condition number, determinant, eigenvalues, eigenvectors, inverse, null vectors, P*L*U factorization or linear system solution are known. Examples include the Fibonacci, Hilbert, Redheffer, Vandermonde, Wathen and Wilkinson matrices.
- test_mat_test
- test_nonlin, an Octave code which implements test problems for the solution of systems of nonlinear equations.
- test_nonlin_test
- test_zero, an Octave code which defines some functions f(x) suitable for testing software that solves a nonlinear equation f(x)=0;
- test_zero_test
- tester, a BASH script which runs the Octave test codes.
- three_body_ode, an Octave code which sets up and solves ordinary differential equations (ODE) that simulate the behavior of three planets, constrained to lie in a plane, and moving under the influence of gravity, by Walter Gander and Jiri Hrebicek.
- three_body_ode_test
- timestamp, an Octave code which prints the current YMDHMS date as a timestamp;
- timestamp_test
- tough_ode, an Octave code which sets up and solves a system of four ordinary differential equations (ODE) which is extremely difficult to solve accurately.
- tough_ode_test
- trapezoidal, an Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method, and fsolve() for the implicit system.
- trapezoidal_test
- trapezoidal_fixed, an Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method, and a fixed point method for the implicit system.
- trapezoidal_fixed_test
- triangulation_boundary, an Octave code which starts with a triangulation of a simple shape, and determines the triangle edges that form the boundary, and a sequence of nodes that trace the boundary.
- triangulation_boundary_test
- trinity, an Octave code which considers the trinity puzzle, a smaller version of the eternity puzzle. The trinity puzzle specifies a region R composed of 144 30-60-90 triangles, and a set of 4 "tiles", T1, T2, T3 and T4, each consisting of 36 30-60-90 triangles, and seeks an arrangement of the four tiles that exactly covers the region.
- trinity_test
- trinity_solution, a MATLAB code which prints or plots a solution to the trinity tiling puzzle, after it has been defined by trinity_lp_automatic() and solved by cplex(). NOT WORKING YET: needs an additional Java library for xmlread().
- trinity_solution_test
- two_body_ode, an Octave code which sets up and solves ordinary differential equations (ODE) which simulate the behavior of two bodies, constrained to lie in a plane, moving under the influence of gravity, with one body much more massive than the other.
- two_body_ode_test
- vanderpol_ode, an Octave code which sets up and solves the van der Pol system of ordinary differential equations (ODE).
- vanderpol_ode_test
- wtime, an Octave code which returns a reading of the wall clock time in seconds.
- wtime_test
- zero, an Octave code which seeks a solution of a scalar nonlinear equation f(x)=0, by Richard Brent.
- zero_test
- zero_rc, an Octave code which seeks a solution of a scalar nonlinear equation f(x)=0, using reverse communication (RC), by Richard Brent.
- zero_rc_test
- zombie_ode, an Octave code which sets up and solves a system of ordinary differential equations (ODE) for a generalized Susceptible-Infected-Recovered (SIR) disease model to simulate a zombie attack, developed by Philip Munz.
- zombie_ode_test