使用R求解ODE

Question

I'm trying to solve an ODE using R as I dont have access to matlab

The equations are

dh/dt = 0.1*v/(pi*(2*10*h-h^2))

v^2 = (-0.1*v/(pi*(2*10*h-h^2))^2) + 2*9.81*h))

---

vdpol <- function (h, v, t) ( 
      list(c (
        -0.1*v/(pi*(2*10*h-h^2)),
          (v^2 = (-0.1*v/(pi*(2*10*h-h^2))^2) + 2*9.81*h))

              ))
library(deSolve)
yini <- (c(h = 20, v=0))
nonstiff <- ode(y = yini, func = vdpol,
                times= seq(0, 30, by = 0.01),
                parms = 1) 

The issues that pops up is:

The number of derivatives returned by func() (4) must equal the length of the initial conditions vector (2)

I'm not why it suggests that 4 derivatives have been inputted when i only out two

Answer 1

IIUC, ode expects a function with a given format. Refer to here

Hence, if you change your vdpol() function to meet the expected format, it should run. The general format is func(t, state, parameters) where state controls for your variables and parameters for other parameters.

vdpol <- function (t, state, parameters) ( 
    with(as.list(c(state)), {
    return(list(c (-0.1*v/(pi*(2*10*h-h^2)),
                  (-0.1*v/(pi*(2*10*h-h^2))^2) + 2*9.81*h)))
    })
)

state = c(h = 10, v = 0)
times= seq(0, 30, by = 0.01)
out <- ode(y = state, times = times, func = vdpol, parms = c())
plot(out)

---