[ Get the code at github ]
We’re using RK4 to solve:
$$ \begin{aligned} \frac{df_1(x)}{dx} =& 1 - f_2(x)\ & \ \frac{df_2(x)}{dx} =& f_1(x) - x \end{aligned} $$
with initial conditions:
$$\begin{aligned} x_0 &= 0\ f_1(x_0) &= 1\ f_2(x_0) &= 0 \end{aligned}$$
in the range $$[0,3]$$.
See the introductory post for details.
As already noted, the code below will be rather idiomatic for each language.
J
[ J is a terse array programming language. It’s on GPLv3 since March 2011 ]
Resisting the temptation to reduce the code to a line of illegible, swear-like bunch of characters, here is the full code in just 8 crystal clear lines.
<{{static/src/the-choice-2-j-and-lisp/rk4.ijs}}[1,15]
Extendable, expandable, short.
For example:
<{{static/src/the-choice-2-j-and-lisp/rk4.ijs}}[16,]
That gives us the vector v
with all the value-pairs $$(x,y1,y2)$$
v
0 1 0
0.01 1.00995 0.00999983
0.02 1.0198 0.0199987
0.03 1.02955 0.0299955
0.04 1.0392 0.0399893
0.05 1.04875 0.0499792
...
2.97 1.98469 0.170752
2.98 1.99303 0.16089
2.99 2.00147 0.151013
3 2.01001 0.14112
which we can conveniently plot:
load 'plot'
'key f1, f2' plot ({. ; (1 { ]) ,: 2 { ]) |: v
LISP
<{{static/src/the-choice-2-j-and-lisp/rk4.cl}}[,16]
For example:
<{{static/src/the-choice-2-j-and-lisp/rk4.cl}}[18,29]
which is indeed the same solution as before:
<{{static/src/the-choice-2-j-and-lisp/rk4.cl}}[31,]
Coming up: R, Fortran, Python, Haskell, Pari/GP, maxima.
Any other languages that you would like to see?