Runge-Kutta using Numerical Recipes

[Vrbic]

Hello,
I try to solve a system of ODE's by Runge-Kutta method from here: https://websites.pmc.ucsc.edu/~fnimmo/eart290c_17/NumericalRecipesinF77.pdf, page 704 in the book (not pdf). Bellow is also a code. In function rk4dumb I don't understand how are implemented differential equations. Input are just initial conditions, steps, amount of equations and function for differentiation. How may I input some real problem there? I track subroutine rk4 it has to be in first input, but the value (v) is taken as a new variable in this subroutine. So I'm a bit confused. Please advise me :-)
Thank you all.

 

[lewando]

First I would advise you to post the code to which you are referring ;)

[ use the insert (+) -> code tool, for best results]

 

[lewando]

Ahh-- nevermind, I see the code now in the link. Do you have a particular system of ODEs in mind?

 

[Vrbic]

First I would advise you to post the code to which you are referring ;)

[ use the insert (+) -> code tool, for best results]

The code is in pdf link which I add (pages 706-708). I don't understand how to use it. I rewrite it as subroutines and I have two functions on the paper and think how to implement it. I know Runge-Kutta but mostly there isn't derivative but function f(x,y) (dy/dx=f(y,x)). Now I'm lost.

 

[Vrbic]

Ahh-- nevermind, I see the code now in the link. Do you have a particular ODE in mind?

I would like to prepare generally. I have system let's say: dy/dx=f(x,y,z) and dz/dx=g(x,y,z). Where I input functions f and g?

 

[lewando]

I am constrained presently. See if this helps for now: https://epublications.bond.edu.au/cgi/viewcontent.cgi?article=1130&context=ejsie

 

[lewando]

Temporarlly out of my constraint (but not for long)-- so the basic concept is running the rk4 with dy/dx to get a Δy. Then do rk4 with dz/dx to get Δz. Now you have a new y and a new z. Repeat the process.

 

[jtbell]

I have system let's say: dy/dx=f(x,y,z) and dz/dx=g(x,y,z). Where I input functions f and g?

See pages 706-707.

You need to write a subroutine named 'derivs' that calculates the right-hand sides of your equations for the derivatives. First, to make things less confusing, re-name your dependent variables so

dy/dx = f(x,y,z) ---> dy₁/dx = f(x,y₁,y₂)
dz/dx = g(x,y,z) ---> dy₂/dx = g(x,y₁,y₂)

Your subroutine 'derivs(x,y,dydx)' receives the value of x and the two y's at which the derivatives are calculated. Note that y and dydx are both arrays, with length 2. y(1) = y₁ and y(2) = y₂. The subroutine must calculate dydx(1) = dy₁/dx = f(x,y₁,y₂) and dydx(2) = dy₂/dx = g(x,y₁,y₂), which will be returned to the subroutine 'rk4'.

 

[Vrbic]

See pages 706-707.

You need to write a subroutine named 'derivs' that calculates the right-hand sides of your equations for the derivatives. First, to make things less confusing, re-name your dependent variables so

dy/dx = f(x,y,z) ---> dy₁/dx = f(x,y₁,y₂)
dz/dx = g(x,y,z) ---> dy₂/dx = g(x,y₁,y₂)

Your subroutine 'derivs(x,y,dydx)' receives the value of x and the two y's at which the derivatives are calculated. Note that y and dydx are both arrays, with length 2. y(1) = y₁ and y(2) = y₂. The subroutine must calculate dydx(1) = dy₁/dx = f(x,y₁,y₂) and dydx(2) = dy₂/dx = g(x,y₁,y₂), which will be returned to the subroutine 'rk4'.

Thaaaaaank you very much, now I understand. I thought that "derivs" is an ordinary function for general derivatives.
Thank you all, solved.