Description Usage Arguments Examples
Euler ODE solver class
Euler generic
Euler constructor when 'ODE' passed
Euler constructor 'missing' is passed
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | Euler(ode, ...)
## S4 method for signature 'Euler'
init(object, stepSize, ...)
## S4 method for signature 'Euler'
step(object, ...)
## S4 method for signature 'Euler'
setStepSize(object, stepSize, ...)
## S4 method for signature 'Euler'
getStepSize(object, ...)
## S4 method for signature 'ODE'
Euler(ode, ...)
## S4 method for signature 'missing'
Euler(ode, ...)
|
ode |
an ODE object |
... |
additional parameters |
object |
an internal object of the class |
stepSize |
the size of the step |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 | # +++++++++++++++++++++++++++++++++++++++++++++++ application: RigidBodyNXFApp.R
# example of a nonstiff system is the system of equations describing
# the motion of a rigid body without external forces.
importFromExamples("RigidBody.R")
# run the application
RigidBodyNXFApp <- function(verbose = FALSE) {
# load the R class that sets up the solver for this application
y1 <- 0 # initial y1 value
y2 <- 1 # initial y2 value
y3 <- 1 # initial y3 value
dt <- 0.01 # delta time for step
body <- RigidBodyNXF(y1, y2, y3)
solver <- Euler(body)
solver <- setStepSize(solver, dt)
rowVector <- vector("list")
i <- 1
# stop loop when the body hits the ground
while (getState(body)[4] <= 12) {
rowVector[[i]] <- list(t = getState(body)[4],
y1 = getState(body)[1],
y2 = getState(body)[2],
y3 = getState(body)[3])
solver <- step(solver)
body <- getODE(solver)
i <- i + 1
}
DT <- data.table::rbindlist(rowVector)
return(DT)
}
# get the data table from the app
solution <- RigidBodyNXFApp()
plot(solution)
# +++++++++++++++++++++++++++++++++++++++++++++++ example: FallingParticleApp.R
# Application that simulates the free fall of a ball using Euler ODE solver
importFromExamples("FallingParticleODE.R") # source the class
FallingParticleODEApp <- function(verbose = FALSE) {
# initial values
initial_y <- 10
initial_v <- 0
dt <- 0.01
ball <- FallingParticleODE(initial_y, initial_v)
solver <- Euler(ball) # set the ODE solver
solver <- setStepSize(solver, dt) # set the step
rowVector <- vector("list")
i <- 1
# stop loop when the ball hits the ground, state[1] is the vertical position
while (getState(ball)[1] > 0) {
rowVector[[i]] <- list(t = getState(ball)[3],
y = getState(ball)[1],
vy = getState(ball)[2])
solver <- step(solver) # move one step at a time
ball <- getODE(solver) # update the ball state
i <- i + 1
}
DT <- data.table::rbindlist(rowVector)
return(DT)
}
# show solution
solution <- FallingParticleODEApp()
plot(solution)
# KeplerVerlet.R
setClass("Kepler", slots = c(
GM = "numeric",
odeSolver = "Euler",
counter = "numeric"
),
contains = c("ODE")
)
setMethod("initialize", "Kepler", function(.Object, ...) {
.Object@GM <- 4 * pi * pi # gravitation constant times combined mass
.Object@state <- vector("numeric", 5) # x, vx, y, vy, t
.Object@odeSolver <- Euler(.Object)
.Object@counter <- 0
return(.Object)
})
setMethod("doStep", "Kepler", function(object, ...) {
# cat("state@doStep=", object@state, "\n")
object@odeSolver <- step(object@odeSolver)
object@state <- object@odeSolver@ode@state
# object@rate <- object@odeSolver@ode@rate
# cat("\t", object@odeSolver@ode@state)
object
})
setMethod("getTime", "Kepler", function(object, ...) {
return(object@state[5])
})
setMethod("getEnergy", "Kepler", function(object, ...) {
ke <- 0.5 * (object@state[2] * object@state[2] +
object@state[4] * object@state[4])
pe <- -object@GM / sqrt(object@state[1] * object@state[1] +
object@state[3] * object@state[3])
return(pe+ke)
})
setMethod("init", "Kepler", function(object, initState, ...) {
object@state <- initState
object@odeSolver <- init(object@odeSolver, getStepSize(object@odeSolver))
object@counter <- 0
object
})
setReplaceMethod("init", "Kepler", function(object, ..., value) {
object@state <- value
object@odeSolver <- init(object@odeSolver, getStepSize(object@odeSolver))
object@counter <- 0
object
})
setMethod("getRate", "Kepler", function(object, state, ...) {
# Computes the rate using the given state.
r2 <- state[1] * state[1] + state[3] * state[3] # distance squared
r3 <- r2 * sqrt(r2) # distance cubed
object@rate[1] <- state[2]
object@rate[2] <- (- object@GM * state[1]) / r3
object@rate[3] <- state[4]
object@rate[4] <- (- object@GM * state[3]) / r3
object@rate[5] <- 1 # time derivative
# object@state <- object@odeSolver@ode@state <- state
# object@state <- state
object@counter <- object@counter + 1
object@rate
})
setMethod("getState", "Kepler", function(object, ...) {
# Gets the state variables.
return(object@state)
})
# constructor
Kepler <- function() {
kepler <- new("Kepler")
return(kepler)
}
# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ example: PlanetApp.R
# Simulation of Earth orbiting around the SUn using the Euler ODE solver
importFromExamples("Planet.R") # source the class
PlanetApp <- function(verbose = FALSE) {
# x = 1, AU or Astronomical Units. Length of semimajor axis or the orbit
# of the Earth around the Sun.
x <- 1; vx <- 0; y <- 0; vy <- 6.28; t <- 0
state <- c(x, vx, y, vy, t)
dt <- 0.01
planet <- Planet()
planet@odeSolver <- setStepSize(planet@odeSolver, dt)
planet <- init(planet, initState = state)
rowvec <- vector("list")
i <- 1
# run infinite loop. stop with ESCAPE.
while (getState(planet)[5] <= 90) { # Earth orbit is 365 days around the sun
rowvec[[i]] <- list(t = getState(planet)[5], # just doing 3 months
x = getState(planet)[1], # to speed up for CRAN
vx = getState(planet)[2],
y = getState(planet)[3],
vy = getState(planet)[4])
for (j in 1:5) { # advances time
planet <- doStep(planet)
}
i <- i + 1
}
DT <- data.table::rbindlist(rowvec)
return(DT)
}
# run the application
solution <- PlanetApp()
select_rows <- seq(1, nrow(solution), 10) # do not overplot
solution <- solution[select_rows,]
plot(solution)
# +++++++++++++++++++++++++++++++++++++++++++++++ application: RigidBodyNXFApp.R
# example of a nonstiff system is the system of equations describing
# the motion of a rigid body without external forces.
importFromExamples("RigidBody.R")
# run the application
RigidBodyNXFApp <- function(verbose = FALSE) {
# load the R class that sets up the solver for this application
y1 <- 0 # initial y1 value
y2 <- 1 # initial y2 value
y3 <- 1 # initial y3 value
dt <- 0.01 # delta time for step
body <- RigidBodyNXF(y1, y2, y3)
solver <- Euler(body)
solver <- setStepSize(solver, dt)
rowVector <- vector("list")
i <- 1
# stop loop when the body hits the ground
while (getState(body)[4] <= 12) {
rowVector[[i]] <- list(t = getState(body)[4],
y1 = getState(body)[1],
y2 = getState(body)[2],
y3 = getState(body)[3])
solver <- step(solver)
body <- getODE(solver)
i <- i + 1
}
DT <- data.table::rbindlist(rowVector)
return(DT)
}
# get the data table from the app
solution <- RigidBodyNXFApp()
plot(solution)
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