add numerical recipes library

lib/nr/ansi/examples/xrk4.c

@@ -0,0 +1,48 @@
+
+/* Driver for routine rk4 */
+
+#include <stdio.h>
+#define NRANSI
+#include "nr.h"
+#include "nrutil.h"
+
+#define N 4
+
+void derivs(float x,float y[],float dydx[])
+{
+	dydx[1] = -y[2];
+	dydx[2]=y[1]-(1.0/x)*y[2];
+	dydx[3]=y[2]-(2.0/x)*y[3];
+	dydx[4]=y[3]-(3.0/x)*y[4];
+}
+
+int main(void)
+{
+	int i,j;
+	float h,x=1.0,*y,*dydx,*yout;
+
+	y=vector(1,N);
+	dydx=vector(1,N);
+	yout=vector(1,N);
+	y[1]=bessj0(x);
+	y[2]=bessj1(x);
+	y[3]=bessj(2,x);
+	y[4]=bessj(3,x);
+	derivs(x,y,dydx);
+	printf("\n%16s %5s %12s %12s %12s\n",
+		"Bessel function:","j0","j1","j3","j4");
+	for (i=1;i<=5;i++) {
+		h=0.2*i;
+		rk4(y,dydx,N,x,h,yout,derivs);
+		printf("\nfor a step size of: %6.2f\n",h);
+		printf("%12s","rk4:");
+		for (j=1;j<=4;j++) printf(" %12.6f",yout[j]);
+		printf("\n%12s %12.6f %12.6f %12.6f %12.6f\n","actual:",
+			bessj0(x+h),bessj1(x+h),bessj(2,x+h),bessj(3,x+h));
+	}
+	free_vector(yout,1,N);
+	free_vector(dydx,1,N);
+	free_vector(y,1,N);
+	return 0;
+}
+#undef NRANSI