DEAD PROJECT

This project is dead, everyone using Julia should use DifferentialEquations.jl instead. It does everything I dreamed of in this package, but better.

DiffEQ.jl

The DiffEQ package is for solving differential equations numerically in Julia. Currently this is in very early development and really only supports using the Runge-Kutta solver which uses the Dormand-Prince (4, 5) method. Ultimately this package aims to have the basic set of general purpose solvers needed to solve ODE, DAE, and BVP's all coded in pure Julia.

If you are looking for a more mature package now, excellent solvers are found in the ODE.jl package (which this code is heavily based on), the Sundials.jl package, and finally the DASSL.jl package.

To install the package run the following from the Julia prompt:

Pkg.clone("https://github.com/gabrielgellner/DiffEQ.jl")

Example Usage

The solvers in DiffEQ are based around using core top level functions for array outputs aode, and continuous extension (interpolating function) dode. Each of these top level functions expects a ODESystem type as its first argument. Currently the only system supported is Dopri54, which represents the memory and functions needed for the solver.

using DiffEQ
using PyPlot

function f(t, y)
    ydot = similar(y)
    ydot[1] = y[2]*y[3]
    ydot[2] = -y[1]*y[3]
    ydot[3] = -0.51*y[1]*y[2]
    ydot
end

tout = linspace(0.0, 12.0, 10)
# Here we define the type in the call, but you could also save the type as a variable
# and then only incur the memory allocation once for all subsequent calls to the solver.
sol = aode(Dopri54(f, [0.0, 1.0, 1.0]), tout; reltol = 1e-4, abstol = 1e-4)

plot(sol.x, sol.y)

# or if you want to have an interpolating function
csol = dode(Dopri54(f, [0.0, 1.0, 1.0]), [0.0, 1.0]; reltol = 1e-4, abstol = 1e-4))

# which can be called at any time between tstart -> tend
csol(0.5)