RK4-class {rODE}

RK4 class

Description

RK4 class

RK4 generic

RK4 class constructor

Usage

RK4(ode, ...)

## S4 method for signature 'RK4'
init(object, stepSize, ...)

## S4 replacement method for signature 'RK4'
init(object, ...) <- value

## S4 method for signature 'RK4'
step(object, ...)

## S4 method for signature 'ODE'
RK4(ode, ...)

Arguments

ode

an ODE object

...

additional parameters

object

internal passing object

stepSize

the size of the step

value

value for the step

Examples

# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~  base class: Projectile.R
# Projectile class to be solved with Euler method


setClass("Projectile", slots = c(
    g = "numeric",
    odeSolver = "RK4"
    ),
    prototype = prototype(
        g = 9.8
    ),
    contains = c("ODE")
    )

setMethod("initialize", "Projectile", function(.Object) {
    .Object@odeSolver <- RK4(.Object)
    return(.Object)
})

setMethod("setStepSize", "Projectile", function(object, stepSize, ...) {
    # use explicit parameter declaration
    # setStepSize generic has two step parameters: stepSize and dt
    object@odeSolver <- setStepSize(object@odeSolver, stepSize)
    object
})


setMethod("step", "Projectile", function(object) {
    object@odeSolver <- step(object@odeSolver)
    object@rate  <- object@odeSolver@ode@rate
    object@state <- object@odeSolver@ode@state
    object
})


setMethod("setState", signature("Projectile"), function(object, x, vx, y, vy, ...) {
    object@state[1] <- x
    object@state[2] <- vx
    object@state[3] <- y
    object@state[4] <- vy
    object@state[5] <- 0     # t + dt
    object@odeSolver@ode@state <- object@state
    object
})


setMethod("getState", "Projectile", function(object) {
    object@state
})


setMethod("getRate", "Projectile", function(object, state, ...) {
    object@rate[1] <- state[2]     # rate of change of x
    object@rate[2] <- 0            # rate of change of vx
    object@rate[3] <- state[4]     # rate of change of y
    object@rate[4] <- - object@g   # rate of change of vy
    object@rate[5] <- 1            # dt/dt = 1

    object@rate
})


# constructor
Projectile <- function()  new("Projectile")
# ++++++++++++++++++++++++++++++++++++++++++++++++++      example: PendulumApp.R
# Simulation of a pendulum using the EulerRichardson ODE solver

suppressPackageStartupMessages(library(ggplot2))

importFromExamples("Pendulum.R")      # source the class

PendulumApp <- function(verbose = FALSE) {
    # initial values
    theta <- 0.2
    thetaDot <- 0
    dt <- 0.1
    pendulum <- Pendulum()
    # pendulum@state[3] <- 0      # set time to zero, t = 0
    pendulum <- setState(pendulum, theta, thetaDot)
    pendulum <- setStepSize(pendulum, dt = dt) # using stepSize in RK4
    pendulum@odeSolver <- setStepSize(pendulum@odeSolver, dt) # set new step size
    rowvec <- vector("list")
    i <- 1
    while (getState(pendulum)[3] <= 40)    {
        rowvec[[i]] <- list(t        = getState(pendulum)[3],    # time
                            theta    = getState(pendulum)[1], # angle
                            thetadot = getState(pendulum)[2]) # derivative of angle
        pendulum <- step(pendulum)
        i <- i + 1
    }
    DT <- data.table::rbindlist(rowvec)
    return(DT)
}
# show solution
solution <- PendulumApp()
plot(solution)
# +++++++++++++++++++++++++++++++++++++++++++++++++++ application: ReactionApp.R
# ReactionApp solves an autocatalytic oscillating chemical
# reaction (Brusselator model) using
# a fourth-order Runge-Kutta algorithm.

importFromExamples("Reaction.R")      # source the class

ReactionApp <- function(verbose = FALSE) {
    X <- 1; Y <- 5;
    dt <- 0.1

    reaction <- Reaction(c(X, Y, 0))
    solver <- RK4(reaction)
    rowvec <- vector("list")
    i <- 1
    while (getState(reaction)[3] < 100) {             # stop at t = 100
        rowvec[[i]] <- list(t = getState(reaction)[3],
                            X = getState(reaction)[1],
                            Y = getState(reaction)[2])
        solver   <- step(solver)
        reaction <- getODE(solver)
        i <-  i + 1
    }
    DT <- data.table::rbindlist(rowvec)
    return(DT)
}


solution <- ReactionApp()
plot(solution)