euler {demodelr}

Euler's method solution for a differential equation.

Description

euler solves a multi-dimensional differential equation with Euler's method. The parameters listed as required are needed See the vignette for detailed examples of usage.

Usage

euler(
  system_eq,
  initial_condition,
  parameters = NULL,
  t_start = 0,
  deltaT = 1,
  n_steps = 1
)

Arguments

system_eq

(REQUIRED) The 1 or multi dimensional system of equations, written in formula notation as a vector (i.e. c(dx ~ f(x,y), dy ~ g(x,y)))

initial_condition

(REQUIRED) Listing of initial conditions, as a vector

parameters

The values of the parameters we are using (optional)

t_start

The starting time point (defaults to t = 0)

deltaT

The timestep length (defaults to 1)

n_steps

The number of timesteps to compute solution (defaults to n_steps = 1)

Value

A tidy of data frame for the calculated solutions and the time

See Also

rk4

Examples

# Define the rate equation:
lynx_hare_eq <- c(
 dHdt ~ r * H - b * H * L,
 dLdt ~ e * b * H * L - d * L
)

# Define the parameters (as a named vector):
lynx_hare_params <- c(r = 2, b = 0.5, e = 0.1, d = 1)

# Define the initial condition (as a named vector):
lynx_hare_init <- c(H = 1, L = 3)

# Define deltaT and the number of time steps:
deltaT <- 0.05
n_steps <- 200

# Compute the solution via Euler's method:
out_solution <- euler(system_eq = lynx_hare_eq,
                     parameters = lynx_hare_params,
                     initial_condition = lynx_hare_init,
                     deltaT = deltaT,
                     n_steps = n_steps
)