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 楼主
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发表于 2015-11-17 22:57:48
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只看该作者
function solve_nonl_single1
! Q3 M* q6 S3 M$ Z' Iclear all;clc- f' y/ q9 A3 j5 Q
format long. ^, F( B q1 ^* ]. a8 [
global a$ t8 s" q" ~/ L: g) |2 m
a_span=linspace(-0.06,0.06,200);
" H5 F: `/ w& j/ t) e( dn=length(a_span);
: j' d, K8 O1 G/ g- qx0=1e-9;
C9 G+ q4 }' D2 U" g6 ~options=optimset('Algorithm','trust-region-dogleg','TolFun',1e-12,'TolX',1e-12);
7 V- `5 p3 g: v' I" rfor i=1:n
1 c+ e; X( x' ia=a_span(i);
8 W Q" C+ n- K e8 p; zx(i)=fsolve(@nonl,x0,options);) t1 Q( i! f4 _
y(i)=nonl(x(i));
/ ~; o6 t9 r9 A2 E( J+ P) lend
0 R* C" N% ^ X' o/ Y- K5 xa_span', x',y'
% H# P# W4 T# qfunction f=nonl(x)
4 i, r+ @# `0 b5 W+ `) @' Oglobal a
, C! a+ w! F5 t# i" X1 |$ s& {f=1/2*(285+60)*3000*sin(x)-1/2*(25*sin(x)*sin(a)+(60-25*cos(x))*cos(a))*3000*sin(x)+60^2*25*sin(x)*a*sin(a)-60^2*25*cos(x)*a*cos(a)-60*285*(25*cos(x)*sin(a)+25*sin(x)*cos(a));
4 ]+ g% Q; c J8 f% T" P$ t2 e' z" y) w* J+ e6 j
运行结果 ans =6 u% s: \/ L0 z& D7 c
-0.060000000000000
% ^2 [: L+ W/ q7 y8 }6 i6 e-0.0593969849246237 |; `; i1 C. n8 p$ g
-0.058793969849246) K& `9 I H% A! T2 a' ~- x; g3 d7 d$ N
-0.058190954773869) m3 F: z; d2 Z: o. H* z& C
-0.057587939698492& V2 \) G1 J0 ]1 D
-0.056984924623116( e) ?8 C; t! @/ E! U0 I# ]3 U
-0.056381909547739
! o- g: ^. ~ X+ W% Z s- G1 m-0.055778894472362/ K# U$ F) }6 ~
-0.055175879396985
! f$ _% p# Z# Q& g* i-0.0545728643216083 r& r9 w% L! Z4 U
-0.053969849246231! ^* ]9 k$ ^& p5 G( S( M% {
-0.053366834170854
6 r" e( b) W# i6 [9 e! f' ^-0.052763819095477: {# s g q) i
-0.052160804020100% }. ^' J2 \0 T% b& Y1 Y# @
-0.051557788944724
4 a5 Q# _- V& B: L- t( {5 N-0.050954773869347( y2 T( ~) X: t z. R
-0.050351758793970% u3 |, b0 m: t- n4 T+ m
-0.0497487437185932 I3 y3 N! F; f5 H7 ^2 {
-0.049145728643216" m; Z# y) L7 b; y2 i3 f% X+ h$ @
-0.048542713567839
/ L$ [/ |$ {( \4 d# }* V-0.047939698492462
% ~! ]; d: v! G0 h k-0.047336683417085& y1 z: T9 k' b- }8 W
-0.0467336683417094 C; C- M) t$ ?$ ~& w& j, s4 X
-0.0461306532663321 u2 y) Z$ o( u! d" a# U- t2 [( z
-0.0455276381909553 H$ n3 w8 S+ ]+ N! T
-0.0449246231155787 o* j- r. B1 b3 g" j, @3 Q$ O
-0.044321608040201' l5 x0 m7 ]: k, p6 f
-0.0437185929648245 }$ h, @. h5 i$ @2 Y' `
-0.043115577889447+ b# v w& T+ {: D
-0.042512562814070/ l7 g* q8 _( @2 m! K7 I
-0.0419095477386930 ` F- M- x# u, p; a, y7 i. h
-0.041306532663317) }) [1 {+ n, y: w
-0.040703517587940
% x" n4 o2 U) F7 Q$ \6 M ~-0.040100502512563
0 }" J; X3 A: y5 [1 G% u) O-0.039497487437186
3 ~# T: @4 S; F( E: @* ~( C5 n-0.038894472361809- }5 T$ U, z. v+ i1 J- G: Y
-0.038291457286432; }8 G+ ?: V8 C
-0.037688442211055
: x1 Q) S) B) r! l-0.037085427135678/ j. b* f' r$ j# ]5 d
-0.0364824120603026 T- d1 R0 ?4 u% J' T& n8 X
-0.0358793969849257 M V8 f" }% G6 q$ V
-0.0352763819095486 u' F: z) i4 P8 _% G; R1 ?
-0.0346733668341716 u2 {$ s6 J5 t; Z$ {4 A% f: D
-0.0340703517587940 }) _- F, k7 u5 S" p, W
-0.0334673366834179 j1 S- o4 t0 u
-0.032864321608040
+ z! \( b0 ^! S( D3 s% @-0.032261306532663
! u8 B U+ E) }3 ^-0.0316582914572865 t+ G k: F) U7 R& a
-0.031055276381910
5 \# i% T& ]& Y( ^1 R1 @-0.030452261306533
; G8 d$ k. e# `! P* [! u) t-0.029849246231156
9 T' n1 r5 P" _ l. u. K-0.029246231155779! K: i$ d$ O3 j/ Z
-0.028643216080402
8 a( ]0 A+ X3 }5 S/ ~) o* t% `% F$ {-0.028040201005025
, l0 G- T q p% C+ D, {-0.0274371859296488 q* H/ w1 U/ U1 N
-0.026834170854271: o: T' b8 b# f& S+ }. c8 x2 h' j
-0.026231155778894
. b% a- a' d9 [7 H; M-0.025628140703518
( r/ r. J; n! \) B( x; m3 D-0.0250251256281414 w$ F6 A& l( F. F; t" E! e
-0.024422110552764. E' E. E4 t! V
-0.023819095477387$ Y; f/ B2 p7 G. u+ j! _% [
-0.023216080402010/ V5 G) A+ c# f! k* s [) \$ U
-0.022613065326633
+ s# A! D! e( M V- d3 z-0.022010050251256
' B: D6 U# ]3 _9 A3 ^. \9 \-0.021407035175879: c: I! q# B4 n. a+ u
-0.020804020100503
8 W% g3 C! [# }& P-0.020201005025126
# _( v! r5 h8 I' ~" y. F-0.0195979899497496 G! q6 t, d0 y3 T6 p
-0.0189949748743727 e" t- Q1 U# B
-0.018391959798995
3 ^$ v* e8 ]5 |7 F* b; s* i-0.017788944723618
( ?; R5 W+ Q3 v$ A-0.017185929648241
# {8 f9 [( E2 h& X8 B! [' v-0.016582914572864
. r) W' m: c; X8 {/ L( P5 n- x W-0.015979899497487' w' B; j) t& R# C0 C$ b" v4 `
-0.015376884422111* q; Q! e4 k, l. j
-0.014773869346734
& u0 {9 _$ v5 v6 l- [. }& ]-0.014170854271357
# R1 |: |' E, Y. O- p, U7 _8 Y' V6 L-0.013567839195980
9 L1 E: f2 s! O9 w-0.0129648241206036 m- D6 ~9 {: h& H2 _9 g d
-0.0123618090452268 R2 z& }+ p- X% T
-0.0117587939698494 m9 Y: j N8 Q: o- Q$ q
-0.011155778894472
3 B2 \8 C# @) g" {8 f9 U" R-0.010552763819095
( n( n# s9 M2 L$ T) V& j-0.009949748743719
, U' u! | M G2 t7 i-0.009346733668342
+ f2 ^; k. Z! \. ^# _-0.008743718592965
5 b. k$ U! N/ T$ |! l/ s! X8 e-0.008140703517588
& u" A- J; p3 x" x$ V; c+ ]( @-0.0075376884422117 Y" a* r) l+ q9 x9 o/ L' V% q
-0.006934673366834' A2 }' _9 t# g( q
-0.006331658291457- p& [/ Q c" n# m- D
-0.005728643216080, Z7 V5 l) Y/ Y- O. Z+ W0 b6 h0 W
-0.005125628140704
% x9 a {* }. s s7 k4 u-0.004522613065327
C9 G$ q! e: a1 n* g" J4 X8 ^-0.0039195979899505 _7 l; @. P# K% c# W
-0.003316582914573
& o _( [7 q* j-0.002713567839196! h) I" T3 {9 {9 h: O
-0.002110552763819+ n4 W* D; A e5 M
-0.001507537688442
/ W5 U$ V, p' n3 o# ~-0.000904522613065
0 V1 ?# q- d: M. V- ~-0.000301507537688, T! H9 c5 f# R& A) z
0.0003015075376888 T d# j! y8 j( E
0.000904522613065
+ w9 ?: f; {( n7 q0.001507537688442
0 `( ]6 {1 b# y6 K( b: L0.002110552763819
: [9 O6 d- P/ r) i, n0.002713567839196
) S* T# w* u* h3 { V0.003316582914573
9 f$ k3 n4 x. G& V5 J0.0039195979899501 V0 k4 q' ?. w, f$ s, J8 b& I9 J
0.004522613065327/ w, l$ N% Y# C) f; }
0.005125628140704
2 A+ F; F' M4 a* I0.0057286432160802 I- V3 z. |$ U6 R$ \+ b9 f0 g0 Z
0.006331658291457L# w! V3 Y& Z2 `. S" d
0.006934673366834/ b$ e1 N- q5 {0 Z
0.007537688442211
8 l% \$ j% N1 ^4 V. m0.008140703517588& I9 ~* l% H2 \+ x# Y) {
0.008743718592965" B+ q6 w( @' h0 w; l& o
0.0093467336683423 E1 ]3 r# G1 i7 ?: e; M
0.009949748743719
2 J0 i) x. n9 D4 C2 }0.010552763819095* `7 N3 ]. n( V% F, O+ y- s
0.011155778894472
+ `8 c. w3 j0 y+ ?/ L8 p) U0.011758793969849
. T0 x- G! Y# ?$ \* f) c( g0.012361809045226$ ?5 l- k3 S+ t2 [9 g
0.012964824120603
/ ?- n. i/ a# Z8 |) z6 x0.013567839195980* H% q! P' H. ?; V& T
0.014170854271357
! i4 t' O/ u& k- O# M' X$ d6 j0.014773869346734
7 V3 v. j5 y7 _2 o/ {1 \0.0153768844221118 l; c2 O* x3 a) b
0.015979899497487
1 o2 ^* I9 C# \$ u8 Q0.016582914572864
' k( O2 E8 P' O) x: ?6 O0.017185929648241) {$ w3 T$ {! C/ [" h0 U
0.017788944723618
0 U% Z D: ?, Y2 y! q2 U+ v0.018391959798995
# |/ ~* m7 E j0.0189949748743728 u8 Z5 T! N: n/ ?
0.019597989949749
2 R( m: p6 A; i9 r" ]& e0.0202010050251265 f- J% p1 ?+ e
0.0208040201005030 F5 W& v, u. h+ U6 b' J
0.0214070351758792 y. c9 S7 ]/ ]1 v6 Q
0.022010050251256, `+ {7 C+ e7 E# |7 J. G
0.022613065326633
2 U5 D2 Y& z m' V5 \0.023216080402010: W v2 B+ _; N8 z$ L0 S# ]
0.023819095477387+ j7 O* Z6 H, n3 Q: d6 K$ [
0.024422110552764
0 _4 q, t, _ H* ^$ r0.025025125628141) V* [9 @) l$ b* N. U. m: W" y: M$ r
0.025628140703518
; U. {1 Z2 B& m& ]5 t2 x/ E0.026231155778894& v; G F$ Q: d! F* k
0.026834170854271: J7 ?5 G( B. P' `/ F
0.027437185929648
5 r. C4 L7 m3 Z0.028040201005025: o' q/ Y' o/ u6 x l4 g% V: T
0.028643216080402
6 @- j- n+ i4 x, w- S* ~0.0292462311557798 l4 {8 H+ Q5 l- y Z* F8 m
0.029849246231156; ^6 U, m4 S" M& H4 K5 q" V
0.030452261306533- @. \, j7 F3 F1 j, r2 l4 I+ Y
0.031055276381910
; H5 x' b9 U. E$ V2 g6 ^0.031658291457286
' D3 n, @/ a3 A' S- L0.032261306532663
5 t9 ~8 `% a# G- w; h2 t0.032864321608040
2 x- E, p' n5 Q8 v/ U! G i0.033467336683417+ I3 v9 r; o! m) C' ]) {
0.034070351758794
5 F* X: n! s+ z, z, l; B, O0.034673366834171
8 u8 B' k; B; ]6 V0.0352763819095481 p1 H' K ]1 G" P; b7 d/ H
0.035879396984925
, ^' r/ J: h& m" L5 k% w' B0.036482412060302
5 {) p7 t; O# x% W0.037085427135678) a* S* }* H5 u% P& K: L7 U8 W3 I9 q
0.037688442211055
4 y: y- U8 Q: F& G7 l& o% f8 y0.038291457286432
" k1 u0 T) d# f0.038894472361809% A# y- o: B* o) X" V
0.039497487437186' t5 y9 B; D$ I6 i
0.040100502512563. g) F* u7 d( l4 N7 q% m/ c
0.040703517587940
/ T0 q7 \; J5 f6 P5 A0.041306532663317
! L* d( t& |' v2 F' Q( T. S0.041909547738693
/ u. Q5 K/ } d2 c+ g+ e" _, E0.042512562814070/ M; X/ | q6 R# J, ~; y
0.043115577889447
; \ {: p* ?! m9 u9 \0 Y) i0.043718592964824; c0 J+ ?8 n6 k4 N
0.044321608040201
& R( |. @, X2 ]% y, f/ `0.044924623115578( n! ]5 _" t; V6 p" [7 d. a
0.045527638190955
0 H0 r% l, j4 [8 C( u! _0.046130653266332/ Q }5 K. Y' M" b$ V$ z
0.046733668341709
- E3 D- x: ^0 M; Y0.047336683417085& E1 R0 E0 h( n% q# a" E8 o
0.047939698492462
' m# m8 f) ?4 E0.0485427135678397 d1 O' E" r& e9 }* q' I
0.049145728643216" A0 d+ M6 R8 ]" J
0.049748743718593: c3 o% y: p1 d' Y, M B% l
0.050351758793970# z% L8 @1 {5 I) \5 m) `% U
0.050954773869347
, ~# p; Y7 w3 i* [, d$ N0.051557788944724
3 T5 l0 u- `" e0.052160804020101, y) O. x6 [+ g: `7 J
0.052763819095477# l; g' c; u! U8 J$ O- d
0.053366834170854
& G0 O3 ]) [; X0.053969849246231! i' K' v. U! [' T, J2 }- W# u
0.0545728643216089 ]1 B7 q' P7 C2 D/ \5 W& \- o# W
0.055175879396985: k" w0 y% p, V' o2 [2 r
0.0557788944723628 e& g5 @! K1 ^/ x) h
0.056381909547739
! D9 B9 q8 u, P; f8 p0.056984924623116$ L6 ~' P7 t- M3 s1 g; E7 |, l- ]
0.057587939698492
+ U! U' H2 i0 s0 g& I0.058190954773869
/ R1 c5 o# n& t- t0.058793969849246
8 w. |, u' J7 e, i5 i% W; Q0.0593969849246236 {7 z" A0 U, u3 I/ q; M, k
0.060000000000000
# x, H8 h- n- E3 g \2 _. D3 u5 C1 e
- b: r6 f% b+ r0 P( m
ans =
# z% W1 ]. Y& ~% @+ H! q5 y
3 H7 s1 v: E! L; C& z; R, \% I-1.0336895406537160 z6 l) L, ~8 I1 _! p1 t( Y6 N$ W
-1.013619827890691, m$ ^3 m* e1 O9 q C4 v' K4 s9 U
-0.994621366531083
" R5 b6 ~7 h' j5 N-0.9765105340395040 @. r# p* N8 x1 D
-0.959151639002957
# y, Q: [5 }' r-0.942440908631668+ x9 M( o1 O j' N' Q
-0.926296779035772
; T8 \0 l' A9 p# T2 o* u, [. X-0.910653694311287' z+ H! Y5 h! Z' r0 E
-0.895457976752101' \8 U1 Y. J; M+ s7 {6 f7 L
-0.880664979264975
. K) h9 y" {. i( x6 ~" K-0.866237063671064, b, }, S& T ]' b. y# @- E
-0.852142129100671
% q. e9 r1 G3 U4 ^3 U6 x7 p-0.838352517460560$ I' P. `8 s% _2 t
-0.824844183890339) P$ y( o# j6 ~/ {- q. i
-0.8115960575464194 T& l5 L) l2 T
-0.798589541746273" O+ f3 m! u: s L
-0.785808117918193
* \$ S w+ C8 T3 ?5 I-0.773237028068739! U) S0 E( c4 B$ P/ z* K3 {
-0.760863017467603
$ E/ v0 @. F) T1 R' C# E0 ^-0.748674124097121
# |- |2 @4 N$ ?' f! p( g-0.736659504835453# `6 R6 ]8 e$ @9 ~
-0.724809290796292& l7 X( J/ U8 o5 j
-0.713114466033284* r4 Z1 D* X V7 J) |1 h
-0.7015667651334527 G$ u% q- t6 n1 l
-0.690158586205827
; F' ^9 [( e- P' A7 P! H& a% t' L-0.678882916512848
' k& G+ b7 c2 T! T( e, u-0.667733268556930* A) f; u2 n$ G' `% j4 ?3 i ^
-0.656703624869929
6 {% l9 z+ _" J/ z-0.645788390090937
& c8 b. H% ^' }5 K2 H1 K3 n$ y$ T-0.634982349182892
5 O. h; V2 \% _0 v7 T% V, J-0.624280630847343
1 F d1 r% N2 C t! d-0.613678675363112, r$ D3 x' V- V/ |
-0.6031722062077235 S7 |( T8 \& w# l ~" ]3 a
-0.592757204927887
% p5 {8 S3 z: H' |( ~-0.582429888812360' k- E+ \, t4 l F
-0.572186690991612. Z- p% a$ d0 l
-0.562024242646965- I: \0 p4 V7 t- P3 \
-0.5519393570600150 Q I3 V( a' B
-0.5419290152728408 f5 w7 j" a0 l) q' ^
-0.531990353162879- r" U. e U* P
-0.522120649763841% |$ F9 t) p% G" I( ?
-0.512317316687512
" Z g* ~# I; [9 E y-0.502577888520921: `; P; N4 M- T7 ^. v/ b4 C
-0.492900014089836
3 a0 u& {9 T1 @-0.4832814484938855 q& [/ g) Y) w. Y" @- c
-0.4737200458304995 l9 K8 ^3 X0 u
-0.464213752535263, l" @4 {5 V9 l3 G
-0.454760601275071# K! S) I f/ O5 ]
-0.445358705338140. T& a: z$ T2 ~
-0.436006253471471
3 o9 D/ r$ [' M& i! `-0.426701505122098
4 d& H2 u; g6 l) K: h/ u9 _* o7 [( _-0.417442786043397
! {' q' H( B; `/ c+ {- s-0.408228484231992' m* }1 ]" V- V6 `4 u+ Z/ t$ l9 b& u
-0.399057046164675
! ]% I) q# g. `/ N$ C" C-0.3899269733079118 r9 t; D2 S# ]! h2 I
-0.380836818875499# s9 ?, b! a" ?& w& x
-0.371785184812454+ T! j6 y" I. ?. a; Y4 D
-0.362770718985392
; L) [' E/ p7 N1 F# |-0.353792112561766
9 e' c4 g- k4 T4 p0 }: p-0.344848097561934
' K% i2 ?6 g" U3 w8 w$ @" V; X-0.335937444569670
, M" W' Q! Z2 e' m9 C# r: s2 A-0.327058960588106
5 ?. J) e$ m& c) N9 D-0.318211487029265
' b$ H% [) X- \: A4 G y- Q- O-0.309393897826506; o, ~4 u2 X/ h- B
-0.300605097660121! N; @/ H. O2 l' u0 U; z- H1 b
-0.291844020287246+ q2 F5 c3 V8 }, n# w
-0.283109626967980( N; V+ G. x5 W/ a ]
-0.274400904980369
: `$ g& B5 |4 o+ |+ \4 p) i-0.265716866217476; Q" ~5 P3 D8 A: W9 W8 Z6 I
-0.257056545860381
6 e/ J: m1 K' [, H& w$ U- I-0.248419001121443
- t. n$ t5 [) ^8 ?" w( B( p* o-0.239803310052597
* }# n2 Y' ^& E7 u# V-0.231208570413935
p2 j! v" h t" V+ y% B$ P-0.222633898598121
+ S2 u* o1 P6 v- }4 T-0.214078428606594
" `' @$ j4 o7 A-0.205541311073791
/ G! \: C- [5 _-0.197021712335900" k' T1 C5 Z: T) e
-0.188518813540922* B* C, d! m, m8 K- l
-0.180031809797061. x, K8 S3 K1 n4 t9 P
-0.171559909356608
8 p- X" y+ y, j& p9 O-0.163102332832782
: E; _, ] L n) J5 B s-0.154658312447061: U( l* h% m4 Q1 k9 Q
-0.146227091304754
$ Z$ R0 K, X) {4 H5 M ^: ?4 |-0.1378079226966917 V3 f: s, N. Z$ ^2 G# x
-0.129400069425041
" x0 ^ {+ \. P-0.121002803151371: U& a9 Z; h+ l3 l2 L( P4 k
-0.112615403765200" o7 I Y' I. E% C) x0 o: N
-0.104237158771362; d2 M0 d3 L1 A8 K3 V* v7 a
-0.095867362694613
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