deSolve & loop to solve a second order differential equation in R?

Question

Hello dear community,

I am trying to solve a second order differential equation for quite some time now. The equation reads:

∂P/∂t = D * ∂^2P/∂x^2

I should run it for several P's; P1= df$col1, P2=df$col2, P3=df$col3 of a data frame and D would be df$col4 and x would be df$col5

I am trying to use "deSolve" for this, but at the moment I don't have much success. I would appreciate your input on how to solve a second order differential equation with R.

Answer 1

Let me try again. The boundary conditions - initial conditions for variable P would be; P1(t=0)= 0.4; P2(t=0)= 4.6; P3(t=0) = 0.37. I would like to think just in a code for the first P1 and then I could apply the same for the following columns of my data.frame.

Using deSolve this is what I got so far: (P1=P)

state <- c(P=0.4)
t <- seq(0,100, by=0.1)
J <- function (t, P, parameters) {
  deltax     <- c (1, rep(1, numboxes - 1)) ##doing a vector
  Fluxx       <- -D * diff (c(0,P,0) /deltax #First derivative
 dP    <- diff(Fluxx)/deltax # second derivative
  list(dP,Fluxx)
} 

**It would also be possible to solve the equation by applying an Eularian method and compute the change in concentration plus the divergence through time.