R: deSolve - partial differential equation
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Could somebody help me with the R package deSolve/ReacTran, which can be used for solving any parabolic partial differential equation:
I have found a similar example in the book
Karline Soetaert, Jeff_Cash, Francesca Mazzia: Solving Partial Differential Equations in R, chapter 9, page 179-181,
where is a solution for the equation:
Online version of book: Solving Partial Differential Equations in R
The PDE and the solution is defined like:
Schrodinger <- function(t, u, parms) {
du <- 1i * tran.1D (C = u, D = 1, dx = xgrid)$dC +
1i * gam * abs(u)ˆ2 * u
list(du) }
N <- 300
xgrid <- setup.grid.1D(-20, 80, N = N)
x <- xgrid$x.mid
out <- ode.1D(y = yini, parms = NULL, func = Schrodinger,
times = times, dimens = 300, method = "adams")
There's an example of the second partial derivative:
tran.1D (C = u, D = 1, dx = xgrid)$dC
but I'm not sure how to define the first partial derivatives in the PDE
and for derivatives by r_e and r_d (more 'xgrid', or ?)
Thank you in advance for any help.
r differential-equations
edited Nov 10 at 18:39
Ethan
8117
asked Nov 10 at 11:14
Ab B Bg Kostroš
112
add a comment |
up vote
2
down vote
favorite
Could somebody help me with the R package deSolve/ReacTran, which can be used for solving any parabolic partial differential equation:
I have found a similar example in the book
Karline Soetaert, Jeff_Cash, Francesca Mazzia: Solving Partial Differential Equations in R, chapter 9, page 179-181,
where is a solution for the equation:
Online version of book: Solving Partial Differential Equations in R
The PDE and the solution is defined like:
Schrodinger <- function(t, u, parms) {
du <- 1i * tran.1D (C = u, D = 1, dx = xgrid)$dC +
1i * gam * abs(u)ˆ2 * u
list(du) }
N <- 300
xgrid <- setup.grid.1D(-20, 80, N = N)
x <- xgrid$x.mid
out <- ode.1D(y = yini, parms = NULL, func = Schrodinger,
times = times, dimens = 300, method = "adams")
There's an example of the second partial derivative:
tran.1D (C = u, D = 1, dx = xgrid)$dC
but I'm not sure how to define the first partial derivatives in the PDE
and for derivatives by r_e and r_d (more 'xgrid', or ?)
Thank you in advance for any help.
r differential-equations
edited Nov 10 at 18:39
Ethan
8117
asked Nov 10 at 11:14
Ab B Bg Kostroš
112
Your PDE is really 2D+time (r_e as x and r_d as y). So you should look more into tran.2D I believe (same goes for grid.2D and ode.2D). Take a look at the full manual cran.r-project.org/web/packages/ReacTran/ReacTran.pdf or cran.r-project.org/web/packages/ReacTran/vignettes/PDE.pdf PS: never triedrso I won't venture at an answer
– PilouPili
Nov 10 at 22:42
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Could somebody help me with the R package deSolve/ReacTran, which can be used for solving any parabolic partial differential equation:
I have found a similar example in the book
Karline Soetaert, Jeff_Cash, Francesca Mazzia: Solving Partial Differential Equations in R, chapter 9, page 179-181,
where is a solution for the equation:
Online version of book: Solving Partial Differential Equations in R
The PDE and the solution is defined like:
Schrodinger <- function(t, u, parms) {
du <- 1i * tran.1D (C = u, D = 1, dx = xgrid)$dC +
1i * gam * abs(u)ˆ2 * u
list(du) }
N <- 300
xgrid <- setup.grid.1D(-20, 80, N = N)
x <- xgrid$x.mid
out <- ode.1D(y = yini, parms = NULL, func = Schrodinger,
times = times, dimens = 300, method = "adams")
There's an example of the second partial derivative:
tran.1D (C = u, D = 1, dx = xgrid)$dC
but I'm not sure how to define the first partial derivatives in the PDE
and for derivatives by r_e and r_d (more 'xgrid', or ?)
Thank you in advance for any help.
r differential-equations
edited Nov 10 at 18:39
Ethan
8117
asked Nov 10 at 11:14
Ab B Bg Kostroš
112
Could somebody help me with the R package deSolve/ReacTran, which can be used for solving any parabolic partial differential equation:
I have found a similar example in the book
Karline Soetaert, Jeff_Cash, Francesca Mazzia: Solving Partial Differential Equations in R, chapter 9, page 179-181,
where is a solution for the equation:
Online version of book: Solving Partial Differential Equations in R
The PDE and the solution is defined like:
Schrodinger <- function(t, u, parms) {
du <- 1i * tran.1D (C = u, D = 1, dx = xgrid)$dC +
1i * gam * abs(u)ˆ2 * u
list(du) }
N <- 300
xgrid <- setup.grid.1D(-20, 80, N = N)
x <- xgrid$x.mid
out <- ode.1D(y = yini, parms = NULL, func = Schrodinger,
times = times, dimens = 300, method = "adams")
There's an example of the second partial derivative:
tran.1D (C = u, D = 1, dx = xgrid)$dC
but I'm not sure how to define the first partial derivatives in the PDE
and for derivatives by r_e and r_d (more 'xgrid', or ?)
Thank you in advance for any help.
r differential-equations
r differential-equations
edited Nov 10 at 18:39
Ethan
8117
asked Nov 10 at 11:14
Ab B Bg Kostroš
112
edited Nov 10 at 18:39
Ethan
8117
asked Nov 10 at 11:14
Ab B Bg Kostroš
112
edited Nov 10 at 18:39
Ethan
8117
edited Nov 10 at 18:39
Ethan
8117
edited Nov 10 at 18:39
Ethan
8117
8117
asked Nov 10 at 11:14
Ab B Bg Kostroš
112
asked Nov 10 at 11:14
Ab B Bg Kostroš
112
asked Nov 10 at 11:14
Ab B Bg Kostroš
112
112
Your PDE is really 2D+time (r_e as x and r_d as y). So you should look more into tran.2D I believe (same goes for grid.2D and ode.2D). Take a look at the full manual cran.r-project.org/web/packages/ReacTran/ReacTran.pdf or cran.r-project.org/web/packages/ReacTran/vignettes/PDE.pdf PS: never triedrso I won't venture at an answer
– PilouPili
Nov 10 at 22:42
add a comment |
Your PDE is really 2D+time (r_e as x and r_d as y). So you should look more into tran.2D I believe (same goes for grid.2D and ode.2D). Take a look at the full manual cran.r-project.org/web/packages/ReacTran/ReacTran.pdf or cran.r-project.org/web/packages/ReacTran/vignettes/PDE.pdf PS: never triedrso I won't venture at an answer
– PilouPili
Nov 10 at 22:42
Your PDE is really 2D+time (r_e as x and r_d as y). So you should look more into tran.2D I believe (same goes for grid.2D and ode.2D). Take a look at the full manual cran.r-project.org/web/packages/ReacTran/ReacTran.pdf or cran.r-project.org/web/packages/ReacTran/vignettes/PDE.pdf PS: never tried
r so I won't venture at an answer– PilouPili
Nov 10 at 22:42
Your PDE is really 2D+time (r_e as x and r_d as y). So you should look more into tran.2D I believe (same goes for grid.2D and ode.2D). Take a look at the full manual cran.r-project.org/web/packages/ReacTran/ReacTran.pdf or cran.r-project.org/web/packages/ReacTran/vignettes/PDE.pdf PS: never tried
r so I won't venture at an answer– PilouPili
Nov 10 at 22:42
add a comment |
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Your PDE is really 2D+time (r_e as x and r_d as y). So you should look more into tran.2D I believe (same goes for grid.2D and ode.2D). Take a look at the full manual cran.r-project.org/web/packages/ReacTran/ReacTran.pdf or cran.r-project.org/web/packages/ReacTran/vignettes/PDE.pdf PS: never tried
rso I won't venture at an answer– PilouPili
Nov 10 at 22:42