Discussion :

[sebulb]

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 :

Sélectionner tout - Visualiser dans une fenêtre à part

solve(X1,X2)

j'obtiens le message suivant :

Warning: Warning, solutions may have been lost

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

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)

[salseropom]

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.

[rostomus]

Salut,

Tu peux nous poster tes deux équations?

[sebulb]

Voici les 2 équations :

Code :

Sélectionner tout - Visualiser dans une fenêtre à part

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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 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 ?

[sebulb]

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