[solve] Résolution d'un système de deux équations

Bonjour,

je dois résoudre un système de 2 équations (X1 et X2) à 2 inconnues (R et t).
Les équations ne sont pas très commodes et lorsque j'utilise la fonction :

Code:

solve(X1,X2)

j'obtiens le message suivant :

Citation:

Warning: Warning, solutions may have been lost

puis les résultats affichés sont loin d'être ceux que j'attends...:cry:

Visiblement, Matlab dois "manquer de mémoire" et tronque des valeurs, ce qui me donne des résultats faux.
Je ne sais pas trop comment résoudre ce problème.
J'avais pensé utiliser la fonction fzero, mais cela implique de connaître où se situent les solutions et je ne sais pas l'utiliser avec un système, seulement avec une équation à une inconnue.

Est-il possible d'utiliser une autre fonction de résolution de système ?
Ou peut-être utiliser plus de précision dans les valeurs ?

Merci d'avance

Matlab 7.4.0.287 (R2007a)

Salut, tu peux utiliser une méthode numérique. Pour résoudre l'équation f(x)=0 où x est un vecteur de R^2 (x=(x1;x2)), utilise la méthode de Newton et toutes ses variantes.

Salut,

Tu peux nous poster tes deux équations?

Voici les 2 équations :

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)

Salut, tes équations n'ont rien de bien compliqué. Utilise la méthode de Newton et c'est gagné. Le calcul de la jacobienne est facile.
Mais je n'ai pas vu de signe "=" Où est ton second membre ?

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

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

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

Sinon, pour la résolution vous avez raison, je vais utiliser Newton-Raphson.
Merci beacoup ;)

Bon ben j'ai essayé de résoudre le sytème avec la méthode de Newton-Raphson mais matlab n'a toujours pas assez de mémoire. Il me dit au bout d'une heure :

Citation:

??? Out of memory

:evilred:

Voici le code que j'ai tapé pour la méthode de Newton (qui marche avec des exemples plus simples)
Code:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 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 tapé à l'arrache mais il marche sur d'autres équations.

Donc je n'arrive toujours pas à résoudre mon système !!!

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

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

Merci d'avance

Salut,

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

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 numérique
maple : calcul symbolique

même si on peut faire de calcul numérique et symbolique avec ces deux logiciels, à chacun son point fort.

J'obtiens X1 et X2 en remplaçant dans 2 équations de départ toutes les variables qui dépendent de R et t pour obtenir 2 équations à 2 inconnues.

Sinon je veux le résultat en numérique pas en symbolique. C'est juste que j'utilise une déclaration de mes variables R et t en symbolique. Mais je devrais obtenir des résultats numériques 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 mémoire pour stocker toutes ses données utiles à cette inversion. :(

Donc j'ai toujours pas trouvé de solutions .................:cry:

Bjr,

je sais pas si ça a un rapport avec ta difficulté à résoudre tes équations, mas des nombres longs comme d'ici dimanche, genre 12035612411181512153 c'est pas courant en alcul numérique. Tu aurais des problèmes d'arrondi que ça m'étonnerais pas.
Code:

1 2 3 4 5 6 7 >> x=12035612411181512153 ; >> y=x+1 ; >> y-x ans = 0
OL