euler {demodelr} R Documentation

## 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

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### 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
)


[Package demodelr version 1.0.1 Index]