Description Usage Arguments Examples
Verlet ODE solver class
Verlet generic
Verlet class constructor ODE
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ode |
an ODE object |
... |
additional parameters |
object |
a class object |
stepSize |
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 | # ++++++++++++++++++++++++++++++++++++++++++++++++++ example: KeplerEnergyApp.R
# Demostration of the use of the Verlet ODE solver
#
importFromExamples("KeplerEnergy.R") # source the class Kepler
KeplerEnergyApp <- function(verbose = FALSE) {
# initial values
x <- 1
vx <- 0
y <- 0
vy <- 2 * pi
dt <- 0.01
tol <- 1e-3
particle <- KeplerEnergy()
# Two ways of initializing the ODE object
# particle <- init(particle, c(x, vx, y, vy, 0))
init(particle) <- c(x, vx, y, vy, 0)
odeSolver <- Verlet(particle)
# Two ways of initializing the solver
# odeSolver <- init(odeSolver, dt)
init(odeSolver) <- dt
particle@odeSolver <- odeSolver
initialEnergy <- getEnergy(particle)
rowVector <- vector("list")
i <- 1
while (getTime(particle) <= 1.20) {
rowVector[[i]] <- list(t = getState(particle)[5],
x = getState(particle)[1],
vx = getState(particle)[2],
y = getState(particle)[3],
vy = getState(particle)[4],
E = getEnergy(particle))
particle <- doStep(particle)
energy <- getEnergy(particle)
i <- i + 1
}
DT <- data.table::rbindlist(rowVector)
return(DT)
}
solution <- KeplerEnergyApp()
plot(solution)
# +++++++++++++++++++++++++++++++++++++++++++++++++++ application: Logistic.R
# Simulates the logistic equation
importFromExamples("Logistic.R")
# Run the application
LogisticApp <- function(verbose = FALSE) {
x <- 0.1
vx <- 0
r <- 2 # Malthusian parameter (rate of maximum population growth)
K <- 10.0 # carrying capacity of the environment
dt <- 0.01; tol <- 1e-3; tmax <- 10
population <- Logistic() # create a Logistic ODE object
# Two ways of initializing the object
# population <- init(population, c(x, vx, 0), r, K)
init(population) <- list(initState = c(x, vx, 0),
r = r,
K = K)
odeSolver <- Verlet(population) # select the solver
# Two ways of initializing the solver
# odeSolver <- init(odeSolver, dt)
init(odeSolver) <- dt
population@odeSolver <- odeSolver
# setSolver(population) <- odeSolver
rowVector <- vector("list")
i <- 1
while (getTime(population) <= tmax) {
rowVector[[i]] <- list(t = getTime(population),
s1 = getState(population)[1],
s2 = getState(population)[2])
population <- doStep(population)
i <- i + 1
}
DT <- data.table::rbindlist(rowVector)
return(DT)
}
# show solution
solution <- LogisticApp()
plot(solution)
# ++++++++++++++++++++++++++++++++++++++++++++++++++ example: KeplerEnergyApp.R
# Demostration of the use of the Verlet ODE solver
#
importFromExamples("KeplerEnergy.R") # source the class Kepler
KeplerEnergyApp <- function(verbose = FALSE) {
# initial values
x <- 1
vx <- 0
y <- 0
vy <- 2 * pi
dt <- 0.01
tol <- 1e-3
particle <- KeplerEnergy()
# Two ways of initializing the ODE object
# particle <- init(particle, c(x, vx, y, vy, 0))
init(particle) <- c(x, vx, y, vy, 0)
odeSolver <- Verlet(particle)
# Two ways of initializing the solver
# odeSolver <- init(odeSolver, dt)
init(odeSolver) <- dt
particle@odeSolver <- odeSolver
initialEnergy <- getEnergy(particle)
rowVector <- vector("list")
i <- 1
while (getTime(particle) <= 1.20) {
rowVector[[i]] <- list(t = getState(particle)[5],
x = getState(particle)[1],
vx = getState(particle)[2],
y = getState(particle)[3],
vy = getState(particle)[4],
E = getEnergy(particle))
particle <- doStep(particle)
energy <- getEnergy(particle)
i <- i + 1
}
DT <- data.table::rbindlist(rowVector)
return(DT)
}
solution <- KeplerEnergyApp()
plot(solution)
# +++++++++++++++++++++++++++++++++++++++++++++++++++ application: Logistic.R
# Simulates the logistic equation
importFromExamples("Logistic.R")
# Run the application
LogisticApp <- function(verbose = FALSE) {
x <- 0.1
vx <- 0
r <- 2 # Malthusian parameter (rate of maximum population growth)
K <- 10.0 # carrying capacity of the environment
dt <- 0.01; tol <- 1e-3; tmax <- 10
population <- Logistic() # create a Logistic ODE object
# Two ways of initializing the object
# population <- init(population, c(x, vx, 0), r, K)
init(population) <- list(initState = c(x, vx, 0),
r = r,
K = K)
odeSolver <- Verlet(population) # select the solver
# Two ways of initializing the solver
# odeSolver <- init(odeSolver, dt)
init(odeSolver) <- dt
population@odeSolver <- odeSolver
# setSolver(population) <- odeSolver
rowVector <- vector("list")
i <- 1
while (getTime(population) <= tmax) {
rowVector[[i]] <- list(t = getTime(population),
s1 = getState(population)[1],
s2 = getState(population)[2])
population <- doStep(population)
i <- i + 1
}
DT <- data.table::rbindlist(rowVector)
return(DT)
}
# show solution
solution <- LogisticApp()
plot(solution)
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