# DormandPrince.jl

Julia-native implementation of the Dormand-Prince 5th and 8th order solvers

## Installation

DormandPrince is a
Julia Language
package. To install DormandPrince,
please open
Julia's interactive session (known as REPL) and press `]`
key in the REPL to use the package mode, then type the following command

pkg> add DormandPrince

## Usage

### Single End-Time

julia> using DormandPrince
# define your ODE, in this case, dy/dx = 0.85y
julia> function fcn(x, y, f)
f[1] = 0.85y[1]
end
# Create a solver object. We will use the 5th order solver and
# start integrating at t = 0.0 with initial value of 19.0
julia> solver = DP5Solver(fcn, 0.0, [19.0])
# Begin integration up to t = 2.1
julia> integrate!(solver, 2.1)
# get_current_state will return the answer
julia> get_current_state(solver)

Both the `DP5Solver`

and `DP8Solver`

's are stateful allowing for memory-efficient integration to future end times from the last integrated end point (e.g. if you chose t = 1.0 as your endpoint you can call `integrate!`

again with t=2.0 and it will "carry forward" the work starting from t = 1.0 instead of requiring you to set things up all over again).

### Multiple End-Times

julia> using DormandPrince
# Define ODE
julia> function fcn(x, y, f)
f[1] = 0.85y[1]
end
# Define times of interest to analyze/perform actions on the solution
julia> times = [1.0, 1.1, 1.9, 2.4]
# Create the solver object, with integration starting from t = 0.0 and initial value of 19.0
julia> solver = DP5Solver(fcn, 0.0, [19.0])
# Empty array to store intermediate values
julia> intermediate_values = []
# Use callback to store intermediate values. The solver object will also be mutated to store the solution
# found at the last time point.
julia> integrate!(solver, times) do time, val
push!(intermediate_values, val[])
end

You may also create a `SolverIterator`

that can then be iterated over. Note that this will require a fresh solver

for (time, value) in SolverIterator(solver, times)
println("Time: ", time, " ", "Value: ", value[])
end

## License

Apache License 2.0