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Ingy döt Net 2026-02-01 16:33:20 -08:00
parent 5150844a7d
commit 4bb20c9b71
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52
Task/Runge-Kutta-method/Ada/runge-kutta-method.ada
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with Ada.Text_IO; use Ada.Text_IO;
with Ada.Numerics.Generic_Elementary_Functions;
procedure RungeKutta is
type Floaty is digits 15;
type Floaty_Array is array (Natural range <>) of Floaty;
package FIO is new Ada.Text_IO.Float_IO(Floaty); use FIO;
type Derivative is access function(t, y : Floaty) return Floaty;
package Math is new Ada.Numerics.Generic_Elementary_Functions (Floaty);
function calc_err (t, calc : Floaty) return Floaty;
procedure Runge (yp_func : Derivative; t, y : in out Floaty_Array;
dt : Floaty) is
dy1, dy2, dy3, dy4 : Floaty;
begin
for n in t'First .. t'Last-1 loop
dy1 := dt * yp_func(t(n), y(n));
dy2 := dt * yp_func(t(n) + dt / 2.0, y(n) + dy1 / 2.0);
dy3 := dt * yp_func(t(n) + dt / 2.0, y(n) + dy2 / 2.0);
dy4 := dt * yp_func(t(n) + dt, y(n) + dy3);
t(n+1) := t(n) + dt;
y(n+1) := y(n) + (dy1 + 2.0 * (dy2 + dy3) + dy4) / 6.0;
end loop;
end Runge;
procedure Print (t, y : Floaty_Array; modnum : Positive) is begin
for i in t'Range loop
if i mod modnum = 0 then
Put("y("); Put (t(i), Exp=>0, Fore=>0, Aft=>1);
Put(") = "); Put (y(i), Exp=>0, Fore=>0, Aft=>8);
Put(" Error:"); Put (calc_err(t(i),y(i)), Aft=>5);
New_Line;
end if;
end loop;
end Print;
function yprime (t, y : Floaty) return Floaty is begin
return t * Math.Sqrt (y);
end yprime;
function calc_err (t, calc : Floaty) return Floaty is
actual : constant Floaty := (t**2 + 4.0)**2 / 16.0;
begin return abs(actual-calc);
end calc_err;
dt : constant Floaty := 0.10;
N : constant Positive := 100;
t_arr, y_arr : Floaty_Array(0 .. N);
begin
t_arr(0) := 0.0;
y_arr(0) := 1.0;
Runge (yprime'Access, t_arr, y_arr, dt);
Print (t_arr, y_arr, 10);
end RungeKutta;