Nothing
### R code from vignette source 'DAEinR.Rnw'
### Encoding: UTF-8
###################################################
### code chunk number 1: preliminaries
###################################################
library(diffEq)
options(prompt = " ")
options(continue = " ")
options(width = 90)
###################################################
### code chunk number 2: DAEinR.Rnw:76-103
###################################################
resdae <- function (t, y, dy, p) {
r1 <- dy[1] - y[2]
r2 <- y[1] - cos(t)
list(c(r1, r2))
}
library(deTestSet)
yini <- c(y1 = cos(0), y2 = -sin(0))
dyini <- c(-sin(0), -cos(0))
times <- seq(from = 0, to = 10, by = 0.1)
index <- c(1, 1, 0)
out1 <- mebdfi(times = times, res = resdae, y = yini,
atol = 1e-10, rtol = 1e-10, dy = dyini,
parms = NULL, nind = index)
max (abs(out1[,"y1"] - cos(times)), abs(out1[,"y2"] + sin(times)))
fundae <- function (t, y, p) {
f1 <- y[2]
f2 <- y[1] - cos(t)
list(c(f1, f2))
}
M <- matrix(nrow = 2, ncol = 2, data = c(1, 0, 0, 0))
out2 <- radau(times = times, fun = fundae, y = yini,
atol = 1e-10, rtol = 1e-10, mass = M,
parms = NULL, nind = index)
max (abs(out2[,"y1"] - cos(times)), abs(out2[,"y2"] + sin(times)))
###################################################
### code chunk number 3: DAEinR.Rnw:108-142
###################################################
implicit <- function(t, y, dy, parms) {
list(t*y^2*dy^3 - y^3*dy^2 + t*(t^2+1)*dy - t^2*y)
}
yini <- sqrt(3/2)
times <- seq(from = 1, to = 10, by = 0.1)
library(rootSolve)
rootfun <- function (dy, y, t)
t*y^2*dy^3 - y^3*dy^2 + t*(t^2+1)*dy - t^2*y
dyini <- multiroot(f = rootfun, start = 0, y = yini,
t = times[1] )$root
dyini
out <- mebdfi(times = times, res = implicit, y = yini,
dy = dyini, parms = NULL)
out2 <- daspk (times = times, res = implicit, y = yini,
dy = dyini, parms = NULL)
max(abs(out [,2]- sqrt(times^2+0.5)))
max(abs(out2[,2]- sqrt(times^2+0.5)))
implicit2 <- function (t, y, p) {
f1 <- y[2]
f2 <- t*y[1]^2*y[2]^3-y[1]^3*y[2]^2+t*(t^2+1)*y[2]-t^2*y[1]
list(c(f1, f2))
}
M <- matrix(nrow = 2, ncol = 2, data = c(1, 0, 0, 0))
yini_li <- c(yini,dyini)
out3 <- radau(times = times, fun = implicit2, y = yini_li,
mass = M, parms = NULL)
out4 <- gamd (times = times, fun = implicit2, y = yini_li,
mass = M, parms = NULL)
max(abs(out3[,2]- sqrt(times^2+0.5)))
max(abs(out4[,2]- sqrt(times^2+0.5)))
###################################################
### code chunk number 4: DAEinR.Rnw:146-164
###################################################
library(deTestSet)
pendulum <- function (t, y, dy, parms) {
list(c(-dy[1] + y[3] ,
-dy[2] + y[4] ,
-dy[3] -y[5]*y[1] ,
-dy[4] -y[5]*y[2] - 9.8,
y[1]^2 + y[2]^2 -1
))
}
yini <- c(x = 1, y = 0, u = 0, v = 1 , lam = 1)
dyini <- c(dx = 0,dy = 1,du = -1,dv = -9.8,dlam = 3*9.8)
times <- seq(from = 0, to = 10, by = 0.01)
index3 <- c(2, 2, 1)
out3 <- mebdfi (y = yini, dy = dyini, res = pendulum,
parms = NULL, times = times,
nind = index3)
###################################################
### code chunk number 5: pendulum
###################################################
plot(out3, lwd = 2)
plot(out3[, 2:3])
mtext(side = 3, outer = TRUE, line = -1.5,
"Pendulum", cex = 1.5)
###################################################
### code chunk number 6: pendulum
###################################################
plot(out3, lwd = 2)
plot(out3[, 2:3])
mtext(side = 3, outer = TRUE, line = -1.5,
"Pendulum", cex = 1.5)
###################################################
### code chunk number 7: DAEinR.Rnw:185-228
###################################################
caraxis <- function(t, y, dy, parms) {
with(as.list(y), {
f <- rep(0, 10)
yb <- r * sin(w * t)
xb <- sqrt(L^2 - yb^2)
Ll <- sqrt(xl^2 + yl^2)
Lr <- sqrt((xr - xb)^2 + (yr - yb)^2)
f[1:4] <- y[5:8]
f[5] <- 1/k*((L0-Ll)*xl/Ll + lam1*xb + 2*lam2*(xl-xr))
f[6] <- 1/k*((L0-Ll)*yl/Ll + lam1*yb + 2*lam2*(yl-yr)) -g
f[7] <- 1/k*((L0-Lr)*(xr - xb)/Lr - 2*lam2*(xl-xr))
f[8] <- 1/k*((L0-Lr)*(yr - yb)/Lr - 2*lam2*(yl-yr)) -g
f[9] <- xb * xl + yb * yl
f[10]<- (xl - xr)^2 + (yl - yr)^2 - L^2
delt <- dy - f
delt[9:10] <- -f[9:10]
list(delt)
})
}
eps <- 0.01; M <- 10; k <- M * eps * eps/2
L <- 1; L0 <- 0.5; r <- 0.1; w <- 10; g <- 9.8
yini <- c(xl = 0, yl = L0, xr = L, yr = L0,
ul = -L0/L, vl = 0, ur = -L0/L, vr = 0,
lam1 = 0, lam2 = 0)
library(rootSolve)
rootfun <- function (dyi, y, t)
unlist(caraxis(t, y, dy = c(dyi, 0, 0),
parms = NULL)) [1:8]
dyini <- multiroot(f = rootfun, start = rep(0,8),
y = yini, t = 0)$root
(dyini <- c(dyini,0,0))
caraxis(t = 0, yini, dyini, NULL)
index <- c(4, 4, 2)
times <- seq(from = 0, to = 3, by = 0.01)
out <- mebdfi(y = yini, dy = dyini, times = times,
res = caraxis, parms = parameter, nind = index)
###################################################
### code chunk number 8: caraxis
###################################################
par(mar = c(4, 4, 3, 2))
plot(out, lwd = 2, mfrow = c(4,3))
plot(out[,c("xl", "yl")], xlab = "xleft", ylab = "yleft",
type = "l", lwd = 2)
plot(out[,c("xr", "yr")], xlab = "xright", ylab = "yright",
type = "l", lwd = 2)
###################################################
### code chunk number 9: caraxis
###################################################
par(mar = c(4, 4, 3, 2))
plot(out, lwd = 2, mfrow = c(4,3))
plot(out[,c("xl", "yl")], xlab = "xleft", ylab = "yleft",
type = "l", lwd = 2)
plot(out[,c("xr", "yr")], xlab = "xright", ylab = "yright",
type = "l", lwd = 2)
###################################################
### code chunk number 10: DAEinR.Rnw:250-293
###################################################
library(deSolve)
Transistor <- function(t, u, du, pars) {
delt <- vector(length = 8)
uin <- 0.1 * sin(200 * pi * t)
g23 <- beta * (exp( (u[2] - u[3]) / uf) - 1)
g56 <- beta * (exp( (u[5] - u[6]) / uf) - 1)
delt[1] <- (u[1] - uin)/R0
delt[2] <- u[2]/R1 + (u[2]-ub)/R2 + (1-alpha) * g23
delt[3] <- u[3]/R3 - g23
delt[4] <- (u[4] - ub) / R4 + alpha * g23
delt[5] <- u[5]/R5 + (u[5]-ub)/R6 + (1-alpha) * g56
delt[6] <- u[6]/R7 - g56
delt[7] <- (u[7] - ub) / R8 + alpha * g56
delt[8] <- u[8]/R9
list(delt)
}
ub <- 6; uf <- 0.026; alpha <- 0.99; beta <- 1e-6; R0 <- 1000
R1 <- R2 <- R3 <- R4 <- R5 <- R6 <- R7 <- R8 <- R9 <- 9000
C1 <- 1e-6; C2 <- 2e-6; C3 <- 3e-6; C4 <- 4e-6; C5 <- 5e-6
mass <- matrix(nrow = 8, ncol = 8, byrow = TRUE, data = c(
-C1,C1, 0, 0, 0, 0, 0, 0,
C1,-C1, 0, 0, 0, 0, 0, 0,
0, 0,-C2, 0, 0, 0, 0, 0,
0, 0, 0,-C3, C3, 0, 0, 0,
0, 0, 0, C3,-C3, 0, 0, 0,
0, 0, 0, 0, 0,-C4, 0, 0,
0, 0, 0, 0, 0, 0,-C5, C5,
0, 0, 0, 0, 0, 0, C5,-C5
))
yini <- c(0, ub/(R2/R1+1), ub/(R2/R1+1),
ub, ub/(R6/R5+1), ub/(R6/R5+1), ub, 0)
names(yini) <- paste("u", 1:8, sep = "")
ind <- c(8, 0, 0)
times <- seq(from = 0, to = 0.2, by = 0.001)
out <- radau(func = Transistor, y = yini, parms = NULL,
times = times, mass = mass, nind = ind)
###################################################
### code chunk number 11: transistor
###################################################
plot(out, lwd = 2, which = c("u1", "u5", "u8"),
mfrow = c(1, 3))
###################################################
### code chunk number 12: transistor
###################################################
plot(out, lwd = 2, which = c("u1", "u5", "u8"),
mfrow = c(1, 3))
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.