Re-entrant SOLVE and INTEG

[Albert Chan]

(12-19-2021 05:25 PM)Thomas Okken Wrote:  That's not finding a root of a function defined using a root; that's finding a minimum of a function defined using a minimum.

If we can ensure "inner" solver always find a root, we can avoid minimum search.
With R2 ≥ R1 ≥ A, and COSH(X) ≥ 1, FNB(A) always find a root.

10 R1=.508 @ R2=.56 @ L=.5 @ B=0
20 DEF FNB(A) @ B=FNROOT(B,L,COSH((L-FVAR)/A)-R2/A) @ FNB=B
30 DISP A,B,FVALUE @ END DEF
40 A=FNROOT(R1,R2,COSH(FNB(FVAR)/FVAR)-R1/FVAR)
50 DISP A,B,FVALUE

>RUN

Code:

 .508                 .272064726623        0
 .56                  .5                   0
 .48745686541         .237253771483        0
 .463767426087        .206176310534        0
 .462131139668        .204309934281        0
 .462106627543        .204282221362        0
 .462106619541        .204282212316        0
 .462106619541        .204282212316        0