numericalSolution function

Numerical solution and plotting

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.

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.

Returns

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.

Examples

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

See Also

ode, plot

Author(s)

Michael J Grayling