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[求助]
求解方程组 已有3人参与
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本人想求解一个八元方程组，MATLAB还不太会用，写的程序如下，可是求出的结果看不懂，求好心人指教啊，新手无金币，还请包涵 g12=9271.1;g21=495.9;T=303.15;R=8.314; syms x11 x21 x12 x22 r11 r21 r12 r22 alfa=0.2; R=8.314; tao12=g12./R./T; tao21=g21./R./T; G12=exp(-alfa*tao12); G21=exp(-alfa*tao12); >> [x11 x21 x12 x22 r11 r21 r12 r22]=solve(r11-exp(x22.^2.*(tao12.*(G12./(x12+x22.*G12)).^2+tao21.*G21./(x22+x12.*G21).^2)),r12-exp(x22.^2.*(tao12.*(G12./(x12+x22.*G12)).^2+tao21.*G21./(x22+x12.*G21).^2)),r21-exp(x11.^2.*(tao21.*(G21./(x21+x11.*G21)).^2+tao12.*G12./(x11+x21.*G12).^2)),r22-exp(x12.^2.*(tao12.*(G12./(x22+x12.*G12)).^2+tao21.*G21./(x12+x22.*G21).^2)),r11*x11-r12*x12,r21*x21-r22*x22,x11+x21-1,x12+x22-1) 八个方程已检查N遍，应该是没有问题的，跪求指导，好捉急 |
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2楼2014-10-10 16:30:14
dingd
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3楼2014-10-10 17:10:48
zhchh008
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g12=9271.1;g21=495.9;T=303.15;R=8.314; syms x11 x21 x12 x22 r11 r21 r12 r22 alfa=0.2; R=8.314; tao12=g12./R./T; tao21=g21./R./T; G12=exp(-alfa*tao12); G21=exp(-alfa*tao12); [x11 x21 x12 x22 r11 r21 r12 r22]=solve(r11-exp(x22.^2.*(tao12.*(G12./(x12+x22.*G12)).^2+tao21.*G21./(x22+x12.*G21).^2)),r12-exp(x22.^2.*(tao12.*(G12./(x12+x22.*G12)).^2+tao21.*G21./(x22+x12.*G21).^2)),r21-exp(x11.^2.*(tao21.*(G21./(x21+x11.*G21)).^2+tao12.*G12./(x11+x21.*G12).^2)),r22-exp(x12.^2.*(tao12.*(G12./(x22+x12.*G12)).^2+tao21.*G21./(x12+x22.*G21).^2)),r11*x11-r12*x12,r21*x21-r22*x22,x11+x21-1,x12+x22-1); A=[x11 x21 x12 x22 r11 r21 r12 r22]; A = [ 1.0, 1.0, 7.0948863464639782514303197424122, 43.498233938038027684388468928734, 1.0, 1.0, 0, 0] |
4楼2014-10-10 17:15:42
kabaisun
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【答案】应助回帖
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感谢参与，应助指数 +1
小指甲123: 金币+3 2014-10-13 19:56:55
感谢参与，应助指数 +1
小指甲123: 金币+3 2014-10-13 19:56:55
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调整了你的代码如下， g12=92711;g21=4959;T=30315;R=8314; syms x11 x21 x12 x22 r11 r21 r12 r22; alfa=02; R=8314; tao12=g12/R/T; tao21=g21/R/T; G12=exp(-alfa*tao12); G21=exp(-alfa*tao12); [x11,x21,x12,x22,r11,r21,r12,r22]=solve(r11-exp(x22^2*(tao12*(G12/(x12+x22*G12))^2+... tao21*G21/(x22+x12*G21)^2)),r12-exp(x22^2*(tao12*(G12/(x12+x22*G12))^2+tao21*G21/(x22+x12*G21)^2)),r21-exp(x11^2*(tao21*(G21/... (x21+x11*G21))^2+tao12*G12/(x11+x21*G12)^2)),r22-exp(x12^2*(tao12*(G12/(x22+x12*G12))^2+... tao21*G21/(x12+x22*G21)^2)),r11*x11-r12*x12,r21*x21-r22*x22,x11+x21-1,x12+x22-1,x11,x21,x12,x22,r11,r21,r12,r22) 得到答案： x11 = 1.0 x21 = 0 x12 = 1.0 x22 = 0 r11 = 1.0 r21 = 1.0003873240019056602666268435283 r12 = 1.0 r22 = 1.0003875801502729735528926509988 |
5楼2014-10-10 17:26:54
zhchh008
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【答案】应助回帖
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clear; clc; x0=[9.42432037654593e-05,0.999905767707224,9.42937118586778e-05,0.999905766727689,47.7567973044437,0.999999997930520,47.7567972904117,0.999999979060034]; options = optimoptions('fsolve','Display','iter','MaxFunEvals',50000,'TolX',1e-20); [x,fval,exitflag,output,jacobian]=fsolve(@myfun,x0,options); function F=myfun(x) g12=9271.1;g21=495.9;T=303.15;R=8.314; alfa=0.2; R=8.314; tao12=g12./R./T; tao21=g21./R./T; G12=exp(-alfa*tao12); G21=exp(-alfa*tao21); F=[x(5)-exp(x(4).^2.*(tao12.*(G12./(x(3)+x(4).*G12)).^2+tao21.*G21./(x(4)+x(3).*G21).^2)); x(7)-exp(x(4).^2.*(tao12.*(G12./(x(3)+x(4).*G12)).^2+tao21.*G21./(x(4)+x(3).*G21).^2)); x(6)-exp(x(1).^2.*(tao21.*(G21./(x(2)+x(1).*G21)).^2+tao12.*G12./(x(1)+x(2).*G12).^2)); x(8)-exp(x(3).^2.*(tao12.*(G12./(x(4)+x(3).*G12)).^2+tao21.*G21./(x(3)+x(4).*G21).^2)); x(5)*x(1)-x(7)*x(3); x(6)*x(2)-x(8)*x(4); x(1)+x(2)-1; x(3)+x(4)-1]; X=3.66844792052684e-06 0.999996331559379 3.66855860668108e-06 0.999996331558969 47.8248544308314 0.999999999999023 47.8248544308243 0.999999999989381 |
6楼2014-10-10 18:01:52
zhchh008
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7楼2014-10-10 18:02:36
zhchh008
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【答案】应助回帖
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g12=9271.1;g21=495.9;T=303.15;R=8.314; syms x11 x21 x12 x22 r11 r21 r12 r22 alfa=0.2; R=8.314; tao12=g12./R./T; tao21=g21./R./T; G12=exp(-alfa*tao12); G21=exp(-alfa*tao21); [x11 x21 x12 x22 r11 r21 r12 r22]=solve(r11-exp(x22.^2.*(tao12.*(G12./(x12+x22.*G12)).^2+tao21.*G21./(x22+x12.*G21).^2)),r12-exp(x22.^2.*(tao12.*(G12./(x12+x22.*G12)).^2+tao21.*G21./(x22+x12.*G21).^2)),r21-exp(x11.^2.*(tao21.*(G21./(x21+x11.*G21)).^2+tao12.*G12./(x11+x21.*G12).^2)),r22-exp(x12.^2.*(tao12.*(G12./(x22+x12.*G12)).^2+tao21.*G21./(x12+x22.*G21).^2)),r11*x11-r12*x12,r21*x21-r22*x22,x11+x21-1,x12+x22-1); A=[x11 x21 x12 x22 r11 r21 r12 r22]; vpa(A,4) [ 1.0, 1.0, 7.0949, 47.828, 1.0, 1.0, 0, 0] |
8楼2014-10-10 18:11:21
dingd
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【答案】应助回帖
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小指甲123: 金币+3, ★有帮助 2014-10-13 19:57:18
小指甲123: 金币+3, ★有帮助 2014-10-13 19:57:18
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似乎多解： 1： r11: 1.0792834745087 x22: 0.241692882646934 x12: 0.758307117353066 r12: 1.0792834745087 r21: 4.21004443723871 x11: 0.758307117353066 x21: 0.241692882646934 r22: 4.21004443723871 2： r11: 47.8276117781295 x22: 0.999999999706249 x12: 2.93751265462444E-10 r12: 47.8276117781295 r21: 1 x11: 2.93751265481594E-10 x21: 0.999999999706249 r22: 1 3： r11: 0.999999999999093 x22: -7.89502076435928E-13 x12: 1.0000000000017 r12: 1.00000000000091 r21: 7.09488634654321 x11: 1.00000000000442 x21: -5.32197232964814E-12 r22: 47.8276119995367 |
9楼2014-10-10 21:16:31
