Discussion :

[sebulb]

Bonjour,

je dois r�soudre un syst�me de 2 �quations (X1 et X2) � 2 inconnues (R et t).
Les �quations ne sont pas tr�s commodes et lorsque j'utilise la fonction :

Code :

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solve(X1,X2)

j'obtiens le message suivant :

Warning: Warning, solutions may have been lost

puis les r�sultats affich�s sont loin d'�tre ceux que j'attends...

Visiblement, Matlab dois "manquer de m�moire" et tronque des valeurs, ce qui me donne des r�sultats faux.
Je ne sais pas trop comment r�soudre ce probl�me.
J'avais pens� utiliser la fonction fzero, mais cela implique de conna�tre o� se situent les solutions et je ne sais pas l'utiliser avec un syst�me, seulement avec une �quation � une inconnue.

Est-il possible d'utiliser une autre fonction de r�solution de syst�me ?
Ou peut-�tre utiliser plus de pr�cision dans les valeurs ?

Merci d'avance

Matlab 7.4.0.287 (R2007a)

[salseropom]

Salut, tu peux utiliser une m�thode num�rique. Pour r�soudre l'�quation f(x)=0 o� x est un vecteur de R^2 (x=(x1;x2)), utilise la m�thode de Newton et toutes ses variantes.

[rostomus]

Salut,

Tu peux nous poster tes deux �quations?

[sebulb]

Voici les 2 �quations :

Code :

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X1 =
 
598459172153623/2374945115996160*pi-1/4*(1637500000000/273*t^2*R*(18/15625-12035612411181512153/72018011619328000000000000000000*R/t^3+(-2491596114225751/1208925819614629174706176+7802383612627838942311038999531524974685067173656264998622535560518887/33625946619946996896066769151862778492368248522481336320000000000000000000000000000000000000000000000000000000000000*R^4/t^12)*R^2/t^2)^(1/2)*(54459784665979693/2880720464773120000000000000/t^3)^(71/25+5388982421036481330682482662376010433/51865939976016628167831715840000000000000000000000000000*R^2/t^6+(-1314906976004109/576460752303423488+370816673790655729637/72018011619328000000000000000000*R/t^3-145327539147378968191217198930338201/103731879952033256335663431680000000000000000000000000000*R^2/t^6)*R/t)+4189214205075361/26388279066624000)/R*(700976274800963/4611686018427387904-47543392013400271989/144036023238656000000000000000000*R/t^3+5910975214708699665410119948329878257/51865939976016628167831715840000000000000000000000000000000*R^2/t^6+(269/20-9931106086422581923189586280125244302614927665228774727671750448507129/538015145919151950337068306429804455877891976359701381120000000000000000000000000000000000000000000000000000*R^4/t^12+768268220905111444642045323725885970696268735253998472449867711616476769362394983151634283596195860399105811649686808509084460611707421929/7236507430960159138002537883147695892287498964704148031336460737147158526674013993670006695302921745490887311360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000*R^8/t^24)*t^2/R^2)^(1/2)*(54459784665979693/2880720464773120000000000000/t^3)^(-143/50+145353165273499800617/72018011619328000000000000000*R/t^3-24168859520652881873269978654761755101/51865939976016628167831715840000000000000000000000000000*R^2/t^6+(-3176444784221283161893747348048820679/51865939976016628167831715840000000000000000000000000*R^2/t^6+18182104765841874964776682764409991119136453041654452933655897411040067/1345037864797879875842670766074511139694729940899253452800000000000000000000000000000000000000000000000000*R^4/t^12-4878621499956665561347657795538707354816420235941206935106533022273106582126843572092971888838896766563/6976165316107640652787016623812415820133010160793401687975328170575665795846845235200000000000000000000000000000000000000000000000000000000000000000000000000*R^6/t^18)*t/R)-(-6550000000000/273*t^2*R^2*(18/15625-12035612411181512153/72018011619328000000000000000000*R/t^3+(-2491596114225751/1208925819614629174706176+7802383612627838942311038999531524974685067173656264998622535560518887/33625946619946996896066769151862778492368248522481336320000000000000000000000000000000000000000000000000000000000000*R^4/t^12)*R^2/t^2)^(1/2)*(54459784665979693/2880720464773120000000000000/t^3)^(71/25+5388982421036481330682482662376010433/51865939976016628167831715840000000000000000000000000000*R^2/t^6+(-1314906976004109/576460752303423488+370816673790655729637/72018011619328000000000000000000*R/t^3-145327539147378968191217198930338201/103731879952033256335663431680000000000000000000000000000*R^2/t^6)*R/t)*(200030789078143412389/288072046477312000000000000000000/t^3-3656915423851393219995322577165449017/207463759904066512671326863360000000000000000000000000000000/t^6+4361054595430220456135594514690220666542632289390039/59764509885442146192643850359054002364088320000000000000000000000000000000000000000000/t^9+930503702839999/2189866660074853547892690386944*t*54459784665979693^(1/5)*2880720464773120000000000000^(4/5)/(1/t^3)^(4/5)/R)/(700976274800963/4611686018427387904-47543392013400271989/144036023238656000000000000000000*R/t^3+5910975214708699665410119948329878257/51865939976016628167831715840000000000000000000000000000000*R^2/t^6+(269/20-9931106086422581923189586280125244302614927665228774727671750448507129/538015145919151950337068306429804455877891976359701381120000000000000000000000000000000000000000000000000000*R^4/t^12+768268220905111444642045323725885970696268735253998472449867711616476769362394983151634283596195860399105811649686808509084460611707421929/7236507430960159138002537883147695892287498964704148031336460737147158526674013993670006695302921745490887311360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000*R^8/t^24)*t^2/R^2)^(1/2)/((54459784665979693/2880720464773120000000000000/t^3)^(-143/50+145353165273499800617/72018011619328000000000000000*R/t^3-24168859520652881873269978654761755101/51865939976016628167831715840000000000000000000000000000*R^2/t^6+(-3176444784221283161893747348048820679/51865939976016628167831715840000000000000000000000000*R^2/t^6+18182104765841874964776682764409991119136453041654452933655897411040067/1345037864797879875842670766074511139694729940899253452800000000000000000000000000000000000000000000000000*R^4/t^12-4878621499956665561347657795538707354816420235941206935106533022273106582126843572092971888838896766563/6976165316107640652787016623812415820133010160793401687975328170575665795846845235200000000000000000000000000000000000000000000000000000000000000000000000000*R^6/t^18)*t/R))+7779969237997099/26388279066624000)*(200030789078143412389/288072046477312000000000000000000/t^3-3656915423851393219995322577165449017/207463759904066512671326863360000000000000000000000000000000/t^6+4361054595430220456135594514690220666542632289390039/59764509885442146192643850359054002364088320000000000000000000000000000000000000000000/t^9+930503702839999/2189866660074853547892690386944*t*54459784665979693^(1/5)*2880720464773120000000000000^(4/5)/(1/t^3)^(4/5)/R)-(1637500000000/273*t^3*(13/500*R/t-3162509803996765/147573952589676412928*R^2/t^2)*(54459784665979693/2880720464773120000000000000/t^3)^(278/125+3085217946327923/2305843009213693952*R/t)-4189214205075361/52776558133248000)*(1/4/R*(700976274800963/4611686018427387904-47543392013400271989/144036023238656000000000000000000*R/t^3+5910975214708699665410119948329878257/51865939976016628167831715840000000000000000000000000000000*R^2/t^6+(269/20-9931106086422581923189586280125244302614927665228774727671750448507129/538015145919151950337068306429804455877891976359701381120000000000000000000000000000000000000000000000000000*R^4/t^12+768268220905111444642045323725885970696268735253998472449867711616476769362394983151634283596195860399105811649686808509084460611707421929/7236507430960159138002537883147695892287498964704148031336460737147158526674013993670006695302921745490887311360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000*R^8/t^24)*t^2/R^2)^(1/2)*(54459784665979693/2880720464773120000000000000/t^3)^(-143/50+145353165273499800617/72018011619328000000000000000*R/t^3-24168859520652881873269978654761755101/51865939976016628167831715840000000000000000000000000000*R^2/t^6+(-3176444784221283161893747348048820679/51865939976016628167831715840000000000000000000000000*R^2/t^6+18182104765841874964776682764409991119136453041654452933655897411040067/1345037864797879875842670766074511139694729940899253452800000000000000000000000000000000000000000000000000*R^4/t^12-4878621499956665561347657795538707354816420235941206935106533022273106582126843572092971888838896766563/6976165316107640652787016623812415820133010160793401687975328170575665795846845235200000000000000000000000000000000000000000000000000000000000000000000000000*R^6/t^18)*t/R)-54459784665979693/23045763718184960000000000000/t^3-18*t/R)^2/(1/4*t*(13/500*R/t-3162509803996765/147573952589676412928*R^2/t^2)*(54459784665979693/2880720464773120000000000000/t^3)^(278/125+3085217946327923/2305843009213693952*R/t)/R^2*(700976274800963/4611686018427387904-47543392013400271989/144036023238656000000000000000000*R/t^3+5910975214708699665410119948329878257/51865939976016628167831715840000000000000000000000000000000*R^2/t^6+(269/20-9931106086422581923189586280125244302614927665228774727671750448507129/538015145919151950337068306429804455877891976359701381120000000000000000000000000000000000000000000000000000*R^4/t^12+768268220905111444642045323725885970696268735253998472449867711616476769362394983151634283596195860399105811649686808509084460611707421929/7236507430960159138002537883147695892287498964704148031336460737147158526674013993670006695302921745490887311360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000*R^8/t^24)*t^2/R^2)^(1/2)*(54459784665979693/2880720464773120000000000000/t^3)^(-143/50+145353165273499800617/72018011619328000000000000000*R/t^3-24168859520652881873269978654761755101/51865939976016628167831715840000000000000000000000000000*R^2/t^6+(-3176444784221283161893747348048820679/51865939976016628167831715840000000000000000000000000*R^2/t^6+18182104765841874964776682764409991119136453041654452933655897411040067/1345037864797879875842670766074511139694729940899253452800000000000000000000000000000000000000000000000000*R^4/t^12-4878621499956665561347657795538707354816420235941206935106533022273106582126843572092971888838896766563/6976165316107640652787016623812415820133010160793401687975328170575665795846845235200000000000000000000000000000000000000000000000000000000000000000000000000*R^6/t^18)*t/R)/(18/15625-12035612411181512153/72018011619328000000000000000000*R/t^3+(-2491596114225751/1208925819614629174706176+7802383612627838942311038999531524974685067173656264998622535560518887/33625946619946996896066769151862778492368248522481336320000000000000000000000000000000000000000000000000000000000000*R^4/t^12)*R^2/t^2)^(1/2)/((54459784665979693/2880720464773120000000000000/t^3)^(71/25+5388982421036481330682482662376010433/51865939976016628167831715840000000000000000000000000000*R^2/t^6+(-1314906976004109/576460752303423488+370816673790655729637/72018011619328000000000000000000*R/t^3-145327539147378968191217198930338201/103731879952033256335663431680000000000000000000000000000*R^2/t^6)*R/t))-54459784665979693/23045763718184960000000000000/t^3-18*t/R)
 
 
 
X2 =
 
-3275000000000/273*t^2*R*(18/15625-12035612411181512153/72018011619328000000000000000000*R/t^3+(-2491596114225751/1208925819614629174706176+7802383612627838942311038999531524974685067173656264998622535560518887/33625946619946996896066769151862778492368248522481336320000000000000000000000000000000000000000000000000000000000000*R^4/t^12)*R^2/t^2)^(1/2)*(54459784665979693/2880720464773120000000000000/t^3)^(71/25+5388982421036481330682482662376010433/51865939976016628167831715840000000000000000000000000000*R^2/t^6+(-1314906976004109/576460752303423488+370816673790655729637/72018011619328000000000000000000*R/t^3-145327539147378968191217198930338201/103731879952033256335663431680000000000000000000000000000*R^2/t^6)*R/t)+1056558429015651/17592186044416/R*(700976274800963/4611686018427387904-47543392013400271989/144036023238656000000000000000000*R/t^3+5910975214708699665410119948329878257/51865939976016628167831715840000000000000000000000000000000*R^2/t^6+(269/20-9931106086422581923189586280125244302614927665228774727671750448507129/538015145919151950337068306429804455877891976359701381120000000000000000000000000000000000000000000000000000*R^4/t^12+768268220905111444642045323725885970696268735253998472449867711616476769362394983151634283596195860399105811649686808509084460611707421929/7236507430960159138002537883147695892287498964704148031336460737147158526674013993670006695302921745490887311360000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000*R^8/t^24)*t^2/R^2)^(1/2)*(54459784665979693/2880720464773120000000000000/t^3)^(-143/50+145353165273499800617/72018011619328000000000000000*R/t^3-24168859520652881873269978654761755101/51865939976016628167831715840000000000000000000000000000*R^2/t^6+(-3176444784221283161893747348048820679/51865939976016628167831715840000000000000000000000000*R^2/t^6+18182104765841874964776682764409991119136453041654452933655897411040067/1345037864797879875842670766074511139694729940899253452800000000000000000000000000000000000000000000000000*R^4/t^12-4878621499956665561347657795538707354816420235941206935106533022273106582126843572092971888838896766563/6976165316107640652787016623812415820133010160793401687975328170575665795846845235200000000000000000000000000000000000000000000000000000000000000000000000000*R^6/t^18)*t/R)

[salseropom]

Salut, tes �quations n'ont rien de bien compliqu�. Utilise la m�thode de Newton et c'est gagn�. Le calcul de la jacobienne est facile.
Mais je n'ai pas vu de signe "=" O� est ton second membre ?

[sebulb]

Il n'y a pas de signe "= " car il me semble que Matlab le met par defaut dans le solve.

C'est � dire : solve(X1,X2) <=> solve(X1=0,X2=0).

Du moins, c'est ce que j'avais compris dans la documentation.

Sinon, pour la r�solution vous avez raison, je vais utiliser Newton-Raphson.
Merci beacoup

[sebulb]

Bon ben j'ai essay� de r�soudre le syt�me avec la m�thode de Newton-Raphson mais matlab n'a toujours pas assez de m�moire. Il me dit au bout d'une heure :

??? Out of memory

Voici le code que j'ai tap� pour la m�thode de Newton (qui marche avec des exemples plus simples)

Code :

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function S=Newton(F1,F2)
 
syms R t
 
F=[F1;F2];
v=[R,t];
S=[0;0];
J=jacobian(F,v);
Jinv=inv(J);
for i=1:2
    v=[S(1),S(2)];
    X1=subs(F1,R,v(1));
    X1=subs(X1,t,v(2));
    X2=subs(F2,R,v(1));
    X2=subs(X2,t,v(2));
    Ji=subs(Jinv,R,v(1));
    Ji=subs(Ji,t,v(2));
 
 
      S=S-Ji*[X1;X2];
end
S=S;

Il est tap� � l'arrache mais il marche sur d'autres �quations.

Donc je n'arrive toujours pas � r�soudre mon syst�me !!!

Peut-�tre que l'utilisation des variables en symboliques n'est pas une bonne chose ?

Sinon, est-ce que quelqu'un aurait une autre id�e (autre algo, logiciel...)

Merci d'avance

[rostomus]

Salut,

Comment as-tu obtenu X1 et X2?
Est ce que tu veux toujours une solution en "symbolique"?

[salseropom]

je ne suis pas un expert du calcul symbolique avec matlab. Mais je sais que Maple est fait pour faire du calcul symbolique.

Selon moi : matlab : calcul num�rique
maple : calcul symbolique

m�me si on peut faire de calcul num�rique et symbolique avec ces deux logiciels, � chacun son point fort.

[sebulb]

J'obtiens X1 et X2 en rempla�ant dans 2 �quations de d�part toutes les variables qui d�pendent de R et t pour obtenir 2 �quations � 2 inconnues.

Sinon je veux le r�sultat en num�rique pas en symbolique. C'est juste que j'utilise une d�claration de mes variables R et t en symbolique. Mais je devrais obtenir des r�sultats num�riques avec Newton (voir meme avec le "solve" de matlab). Donc maple n'est pas utile ici.

Merci quand meme.

En fait matlab n'arrive pas a inverser la matrice jacobienne dans mon algo de Newton car il ne dispose pas d'assez de m�moire pour stocker toutes ses donn�es utiles � cette inversion.

Donc j'ai toujours pas trouv� de solutions .................

[ol9245]

Bjr,

je sais pas si �a a un rapport avec ta difficult� � r�soudre tes �quations, mas des nombres longs comme d'ici dimanche, genre 12035612411181512153 c'est pas courant en alcul num�rique. Tu aurais des probl�mes d'arrondi que �a m'�tonnerais pas.

Code :

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>> x=12035612411181512153  ;
>> y=x+1 ;
>> y-x
 
ans =
 
     0

OL