用多组初始条件求解R中的ODE

Question

I would like to run solve & plot my ode solution to the following, three different times, chaning a single initial condition each time. I would like to solve for q.0 = 16, q.0 = 20, q.0 = 18.

(It would be nice if this plotted all in a matrix..! Thanks in advance)

rm(list = ls())
par(mfrow = c(1,1))

D = 6 ; A = pi* D^2 / 4 ;


# ODE solver
library(deSolve)


parameters <- c(A, 
                k = (16/sqrt(5)),
                q.0 = 16,
                h.0 = 5
                )

state <- c(h = 5)

Model <- function(t, state, parameters) {
  with(as.list(c(state, parameters)),{
         # rate of change
           dh <- q.0/A - k/A * h^(1/2)

           # return the rate of change
           list(c(dh))
       })   # end with(as.list ...
   }

times <- seq(0, 100, 1)

out <- ode(y = state, times = times, func = Model, parms = parameters)

par(oma = c(0, 0, 3, 0))
plot(out, xlab = "time", ylab = "-")
plot(out[, "time"], out[, "h"], pch = ".", 
     xlab = "time [h]",
     ylab = "Height [ft]")
mtext(outer = TRUE, side = 3, "Variable Holdup Tank Model", cex = 1.5)

write.table(out, "mydataCSTR.txt", sep="\t")

Answer 1

或者，并且仍然很简单：以q.0的第一个值运行它，但使用lines绘制其他两个运行图，以便您可以在同一图形上看到所有三个解决方案。