Added translation

code/info2/rk4.h

@@ -1,8 +1,5 @@
-#include <math.h>
-
-// maksymalna liczba rownan
-// maksimum number of the first order ODE's
-#define MAXN 100
+#ifndef __RK4_H__
+#define __RK4_H__
 
 // --------------------------------------------------------------------------
 // Funkcja wykonuje, metoda Rungego-Kutty IV-ego rzedu,
@@ -16,33 +13,23 @@
 // h  - krok calkowania
 // fun(x,y) - nazwa funkcji obliczajacej prawe strony
 // y1 - obliczona wartosc zmiennej zaleznej w punkcie x0+h
+
 // --------------------------------------------------------------------------
 // Using IV-th order Runge-Kutta method, function performs
-// one integration/time step during solution of the one first-order ODE 
+// one integration/time step during solution of the one first-order ODE
 // (initial value problem):
 //
 //  dy/dx = fun(x,y),    y(x0)=y0
 //
 // Parameters:
-// x0 - initial value of independent variable (time) 
+// x0 - initial value of independent variable (time)
 // y0 - initial value of dependent variable (unknown function y())
-// h  - integration/time step size 
+// h  - integration/time step size
 // fun(x,y) - name of the function computing the right hand side of the equation
-// 
+//
 // rk4() returns y1 - value of dependent variable at point/time x0+h
 //
-double rk4(double x0, double y0, double h, double (*fun)(double, double))
-{
-  double y1;
-  double k1,k2,k3,k4;
-  k1 = h*fun(x0     ,y0      );
-  k2 = h*fun(x0+h/2.,y0+k1/2.);
-  k3 = h*fun(x0+h/2.,y0+k2/2.);
-  k4 = h*fun(x0+h   ,y0+k3   );
-  y1 = y0 + (k1+2.*k2+2.*k3+k4)/6.;
-  return y1;
-}
-
+double rk4(double x0, double y0, double h, double (*fun)(double, double));
 
 // --------------------------------------------------------------------------
 // Funkcja wykonuje, metoda Rungego-Kutty IV-tego rzedu,
@@ -54,62 +41,31 @@ double rk4(double x0, double y0, double h, double (*fun)(double, double))
 // x0 - wartosc startowa zm. niezaleznej
 // y0 - wartosc startowa zm. zaleznej (tablica n-elementowa)
 // h  - krok calkowania
-// n  - liczba rownan
+// n  - liczba rownań
 // fun(x,y,prawastr) - nazwa funkcji obliczajacej prawe strony
 // y1 - obliczona wartosc zmiennej zaleznej w punkcie x0+h
 //      (tablica n-elementowa)
+
 // ------------------------------------------------------------------------------
 // Using IV-th order Runge-Kutta method, function performs
-// one integration/time step during solution of the set of  
+// one integration/time step during solution of the set of
 // the n first-order ODE's:
 //
 //  dY/dx = Fun(x,Y),    Y(x0)=y0[]   where Y,Fun,y0 are vectors
 //
 // Parameters:
-// x0   - initial value of independent variable (time) 
+// x0   - initial value of independent variable (time)
 // y0[] - initial values of dependent variables (n-element array)
-// h    - integration/time step size 
+// h    - integration/time step size
 // n    - number of the first-order ODE's (size of arrays y0[] and y1[])
 //
-// fun(x0,y0,k) - name of the function computing the right hand sides 
-//                of the set of n equations, it takes x0, y0[] and returns 
+// fun(x0,y0,k) - name of the function computing the right hand sides
+//                of the set of n equations, it takes x0, y0[] and returns
 //                vector k[] containing evaluated right hand sides
-// 
-// vrk4() result is y1[] array with values of dependent variables 
+//
+// vrk4() result is y1[] array with values of dependent variables
 // at point/time x0+h
 //
-void vrk4(double x0, double y0[], double h, int n, void (*fun)(double, double*, double*), double y1[])
-{
-  int i;
-  double k1[MAXN], k2[MAXN], k3[MAXN], k4[MAXN];
-  double ytmp[MAXN];
-
-  fun(x0, y0, k1);
-  for (i = 0; i < n; ++i)
-  {
-    k1[i] *= h;
-    ytmp[i] = y0[i] + k1[i]/2.0;
-  }
-
-  fun(x0+h/2.0, ytmp, k2);
-  for (i = 0; i < n; ++i)
-  {
-    k2[i] *= h;
-    ytmp[i] = y0[i] + k2[i]/2.0;
-  }
-
-  fun(x0+h/2.0, ytmp, k3);
-  for (i = 0; i < n; ++i)
-  {
-    k3[i] *= h;
-    ytmp[i] = y0[i] + k3[i];
-  }
-
-  fun(x0+h, ytmp, k4);
-  for (i = 0; i < n; ++i)
-    k4[i] *= h;
-
-  for (i = 0; i < n; ++i)
-    y1[i] = y0[i] + (k1[i] + 2.*k2[i] + 2.*k3[i] + k4[i])/6.;
-}
+void vrk4(double x0, double y0[], double h, int n, void (*fun)(double, double*, double*), double y1[]);
 
+#endif