numericalSolution: Numerical solution and plotting
In phaseR: Phase Plane Analysis of One- And Two-Dimensional Autonomous ODE Systems

numericalSolution

R Documentation

Numerical solution and plotting

Description

Numerically solves a two-dimensional autonomous ODE system for a given initial condition, using ode from the package deSolve. It then plots the dependent variables against the independent variable.

Usage

numericalSolution(
  deriv,
  y0 = NULL,
  tlim,
  tstep = 0.01,
  parameters = NULL,
  type = "one",
  col = c("red", "blue"),
  add.grid = TRUE,
  add.legend = TRUE,
  state.names = c("x", "y"),
  xlab = "t",
  ylab = state.names,
  method = "ode45",
  ...
)

Arguments

`deriv`	A function computing the derivative at a point for the ODE system to be analysed. Discussion of the required structure of these functions can be found in the package vignette, or in the help file for the function `ode`.
`y0`	The initial condition. Should be a `numeric` `vector` of `length` two reflecting the location of the two dependent variables initially.
`tlim`	Sets the limits of the independent variable for which the solution should be plotted. Should be a `numeric` `vector` of `length` two. If `tlim[2] > tlim[1]`, then `tstep` should be negative to indicate a backwards trajectory.
`tstep`	The step length of the independent variable, used in numerical integration. Decreasing the absolute magnitude of `tstep` theoretically makes the numerical integration more accurate, but increases computation time. Defaults to `0.01`.
`parameters`	Parameters of the ODE system, to be passed to `deriv`. Supplied as a `numeric` `vector`; the order of the parameters can be found from the `deriv` file. Defaults to `NULL`.
`type`	If set to `"one"` the trajectories are plotted on the same graph. If set to `"two"` they are plotted on separate graphs. Defaults to `"one"`.
`col`	Sets the colours of the trajectories of the two dependent variables. Should be a `character` `vector` of `length` two. Will be reset accordingly if it is of the wrong `length`. Defaults to `c("red", "blue")`.
`add.grid`	Logical. If `TRUE`, grids are added to the plots. Defaults to `TRUE`.
`add.legend`	Logical. If `TRUE`, a `legend` is added to the plots. Defaults to `TRUE`.
`state.names`	The state names for `ode` functions that do not use positional states.
`xlab`	Label for the x-axis of the resulting plot.
`ylab`	Label for the y-axis of the resulting plot.
`method`	Passed to `ode`. See there for further details. Defaults to `"ode45"`.
`...`	Additional arguments to be passed to `plot`.

Value

Returns a list with the following components:

`add.grid`	As per input.
`add.legend`	As per input.
`col`	As per input, but with possible editing if a `character` `vector` of the wrong `length` was supplied.
`deriv`	As per input.
`method`	As per input.
`parameters`	As per input.
`t`	A `numeric` `vector` containing the values of the independent variable at each integration step.
`tlim`	As per input.
`tstep`	As per input.
`x`	A `numeric` `vector` containing the numerically computed values of the first dependent variable at each integration step.
`y`	A `numeric` `vector` containing the numerically computed values of the second dependent variable at each integration step.
`y0`	As per input.

Author(s)

Michael J Grayling

Examples

# A two-dimensional autonomous ODE system, vanDerPol.
vanDerPol_numericalSolution <- numericalSolution(vanDerPol,
                                                 y0         = c(4, 2),
                                                 tlim       = c(0, 100),
                                                 parameters = 3)

phaseR documentation built on Sept. 2, 2022, 5:07 p.m.