📄 mjyzo_cpp.txt
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/********************************************************************
* Compute the zeros of Bessel functions Jn(x), Yn(x), and their *
* derivatives using subroutine JYZO *
* ----------------------------------------------------------------- *
* SAMPLE RUN: *
* (Compute 10 zeroes for n=1). *
* *
* Please enter order n and number of zeroes: 1 10 *
* *
* Zeros of Bessel functions Jn(x), Yn(x) and their derivatives *
* ( n = 1 ) *
* m jnm j'nm ynm y'nm *
* ----------------------------------------------------------- *
* 1 3.8317060 1.8411838 2.1971413 3.6830229 *
* 2 7.0155867 5.3314428 5.4296810 6.9415000 *
* 3 10.1734681 8.5363164 8.5960059 10.1234047 *
* 4 13.3236919 11.7060049 11.7491548 13.2857582 *
* 5 16.4706301 14.8635886 14.8974421 16.4400580 *
* 6 19.6158585 18.0155279 18.0434023 19.5902418 *
* 7 22.7600844 21.1643699 21.1880689 22.7380347 *
* 8 25.9036721 24.3113269 24.3319426 25.8843146 *
* 9 29.0468285 27.4570506 27.4752950 29.0295758 *
* 10 32.1896799 30.6019230 30.6182865 32.1741182 *
* ----------------------------------------------------------- *
* *
* ----------------------------------------------------------------- *
* Ref.: www.esrf.fr/computing/expg/libraries/smf/PROGRAMS/MJYZO.for *
* *
* C++ Release 1.0 By J-P Moreau, Paris. *
********************************************************************/
#include <stdio.h>
#include <math.h>
#define NMAX 101
double RJ0[NMAX], RJ1[NMAX], RY0[NMAX], RY1[NMAX];
int M, N, NT;
char res[2];
void JYNDD(int N, double X, double *BJN, double *DJN,
double *FJN, double *BYN, double *DYN, double *FYN);
void JYZO(int N, int NT, double *RJ0, double *RJ1, double *RY0, double *RY1) {
/* ========================================================
! Purpose: Compute the zeros of Bessel functions Jn(x),
! Yn(x), and their derivatives
! Input : n --- Order of Bessel functions (0 to 100)
! NT --- Number of zeros (roots)
! Output: RJ0(L) --- L-th zero of Jn(x), L=1,2,...,NT
! RJ1(L) --- L-th zero of Jn"(x), L=1,2,...,NT
! RY0(L) --- L-th zero of Yn(x), L=1,2,...,NT
! RY1(L) --- L-th zero of Yn"(x), L=1,2,...,NT
! Routine called: JYNDD for computing Jn(x), Yn(x), and
! their first and second derivatives
! ======================================================== */
// Labels: e10, e15, e20, e25
double BJN,DJN,FJN,BYN,DYN,FYN;
double X, X0;
int L;
if (N <= 20)
X = 2.82141+1.15859*N;
else
X = N + pow(1.85576*N,0.33333) + pow(1.03315/N,0.33333);
L=0;
e10: X0=X;
JYNDD(N,X,&BJN,&DJN,&FJN,&BYN,&DYN,&FYN);
X -= BJN/DJN;
if (fabs(X-X0) > 1e-9) goto e10;
L++;
RJ0[L]=X;
X=X+3.1416+(0.0972+0.0679*N-0.000354*N*N)/L;
if (L < NT) goto e10;
if (N <= 20)
X=0.961587+1.07703*N;
else
X=N + pow(0.80861*N,0.33333) + pow(0.07249/N,0.33333);
if (N == 0) X=3.8317;
L=0;
e15: X0=X;
JYNDD(N,X,&BJN,&DJN,&FJN,&BYN,&DYN,&FYN);
X=X-DJN/FJN;
if (fabs(X-X0) > 1e-9) goto e15;
L++;
RJ1[L]=X;
X=X+3.1416+(0.4955+0.0915*N-0.000435*N*N)/L;
if (L < NT) goto e15;
if (N <= 20)
X=1.19477+1.08933*N;
else
X=N + pow(0.93158*N,0.33333) + pow(0.26035/N,0.33333);
L=0;
e20: X0=X;
JYNDD(N,X,&BJN,&DJN,&FJN,&BYN,&DYN,&FYN);
X=X-BYN/DYN;
if (fabs(X-X0) > 1e-9) goto e20;
L++;
RY0[L]=X;
X=X+3.1416+(0.312+0.0852*N-0.000403*N*N)/L;
if (L < NT) goto e20;
if (N <= 20)
X=2.67257+1.16099*N;
else
X=N + pow(1.8211*N,0.33333) + pow(0.94001/N,0.33333);
L=0;
e25: X0=X;
JYNDD(N,X,&BJN,&DJN,&FJN,&BYN,&DYN,&FYN);
X=X-DYN/FYN;
if (fabs(X-X0) > 1e-9) goto e25;
L++;
RY1[L]=X;
X=X+3.1416+(0.197+0.0643*N-0.000286*N*N)/L;
if (L < NT) goto e25;
}
void JYNDD(int N, double X, double *BJN, double *DJN,
double *FJN, double *BYN, double *DYN, double *FYN) {
/* =============================================================
! Purpose: Compute Bessel functions Jn(x) and Yn(x), and
! their first and second derivatives
! Input: x --- Argument of Jn(x) and Yn(x) ( x > 0 )
! n --- Order of Jn(x) and Yn(x)
! Output: BJN --- Jn(x)
! DJN --- Jn'(x)
! FJN --- Jn"(x)
! BYN --- Yn(x)
! DYN --- Yn'(x)
! FYN --- Yn"(x)
! ============================================================= */
// Label e15
double BJ[NMAX], BY[NMAX];
int K,M, MT, NT;
double F,F0,F1,BS,SU;
double E0,EC,S1;
for (NT=1; NT<=900; NT++) {
MT=(int) floor(0.5*log10(6.28*NT)-NT*log10(1.36*fabs(X)/NT));
if (MT > 20) goto e15;
}
e15: M=NT;
BS=0.0;
F0=0.0;
F1=1e-35;
SU=0.0;
for (K=M; K>=0; K--) {
F=2.0*(K+1.0)*F1/X-F0;
if (K <= N+1) BJ[K+1]=F;
if ((K % 2) == 0) {
BS=BS+2.0*F;
if (K != 0)
if (((K / 2) % 2) == 0)
SU += F/K;
else
SU -= F/K;
}
F0=F1;
F1=F;
}
for (K=0; K<=N+1; K++) BJ[K+1] /= BS-F;
*BJN=BJ[N+1];
EC=0.5772156649015329;
E0=0.3183098861837907;
S1=2.0*E0*(log(X/2.0)+EC)*BJ[1];
F0=S1-8.0*E0*SU/(BS-F);
F1=(BJ[2]*F0-2.0*E0/X)/BJ[1];
BY[1]=F0;
BY[2]=F1;
for (K=2; K<=N+1; K++) {
F=2.0*(K-1.0)*F1/X-F0;
BY[K+1]=F;
F0=F1;
F1=F;
}
*BYN=BY[N+1];
*DJN=-BJ[N+2]+N*BJ[N+1]/X;
*DYN=-BY[N+2]+N*BY[N+1]/X;
*FJN=(N*N/(X*X)-1.0)*(*BJN)-*DJN/X;
*FYN=(N*N/(X*X)-1.0)*(*BYN)-*DYN/X;
}
void main() {
printf("\n Please enter order n and number of zeroes: ");
scanf("%d %d", &N, &NT);
JYZO(N,NT,RJ0,RJ1,RY0,RY1);
printf("\n Zeros of Bessel functions Jn(x), Yn(x), and their derivatives");
printf("\n ( n = %d )", N);
printf("\n m jnm j'nm ynm y'nm");
printf("\n -----------------------------------------------------------\n");
for (M=1; M<=NT; M++)
printf(" %3d%14.7f%14.7f%14.7f%14.7f\n", M, RJ0[M], RJ1[M], RY0[M], RY1[M]);
printf(" -----------------------------------------------------------\n\n");
}
// End of file mjyzo.cpp
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