Module rk4_tl_ad

A classical fourth order Runge-Kutta scheme for the TL/AD model.

Butcher tableau:

0   |
1/2 | 1/2
1/2 | 0    1/2
1   | 0    0    1
    +-------------------
      1/6  1/3  1/3  1/6

Functions

rk4_tl_ad (n) Create a TL/AD integrator for n-arrays.
integrator (y, deltay, f, f_tl, t, dt, ynew, deltaynew) Integrator for n-arrays


Functions

rk4_tl_ad (n)
Create a TL/AD integrator for n-arrays. y is also evolved to calculate the correct TL. Note that the function f_tl has more arguments than a regular integrator. You need to pass both has both the trajectory y (also ystar) and the perturbation deltay: f_tl(t,y,deltay,buf) instead of f(t,y,buf)

Parameters:

  • n number of variables (length of the array)

Returns:

    Integrator for n-arrays
integrator (y, deltay, f, f_tl, t, dt, ynew, deltaynew)
Integrator for n-arrays

Parameters:

  • y variables at time t
  • deltay perturbation at time t
  • f function to calculate the time derivatives of the variables
  • f_tl function to calculate the time derivatives of the tangent linear model
  • t time
  • dt time integration step
  • ynew n-array (buffer) to store the new y value
  • deltaynew n-array (buffer) to store the new perturbation value

Returns:

  1. t+dt (incremented time)
  2. ynew array with variables at time t+dt
  3. deltaynew array with perturbation at time t+dt
generated by LDoc Last updated 2017-01-05 15:53:41