solve seven nonlinear equations with seven variables in matlab

Question

Haris Hameed 2013-4-12

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/71792-solve-seven-nonlinear-equations-with-seven-variables-in-matlab

hi, I have the following seven equations with seven varibles, I use syms to solve them

syms Eo a b t1 e1 t2 e2
ans = solve('(Eo*0.01)+(a*0.01^2)+(b*0.01^3)+(t1*e1*0.001*(1-exp(-0.1/t1)))+(t2*e2*(1-exp(-0.1/t2)))=30', ...
            '(Eo*0.02)+(a*0.02^2)+(b*0.02^3)+(t1*e1*0.001*(1-exp(-0.2/t1)))+(t2*e2*(1-exp(-0.2/t2)))=62', ...
            '(Eo*0.03)+(a*0.03^2)+(b*0.03^3)+(t1*e1*0.001*(1-exp(-0.3/t1)))+(t2*e2*(1-exp(-0.3/t2)))=86', ...
            '(Eo*0.04)+(a*0.04^2)+(b*0.04^3)+(t1*e1*0.001*(1-exp(-0.4/t1)))+(t2*e2*(1-exp(-0.4/t2)))=101', ...
            '(Eo*0.05)+(a*0.05^2)+(b*0.05^3)+(t1*e1*0.001*(1-exp(-0.5/t1)))+(t2*e2*(1-exp(-0.5/t2)))=108', ...
            '(Eo*0.06)+(a*0.06^2)+(b*0.06^3)+(t1*e1*0.001*(1-exp(-0.6/t1)))+(t2*e2*(1-exp(-0.6/t2)))=111', ...
            '(Eo*0.07)+(a*0.07^2)+(b*0.07^3)+(t1*e1*0.001*(1-exp(-0.7/t1)))+(t2*e2*(1-exp(-0.7/t2)))=111', ...
            'Eo','a','b','t1','e1','t2','e2')

I get this answer

Warning: Explicit solution could not be found. > In solve at 83 In Untitled at 5 ans = [ empty sym ]

please help!

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Answer 1

Walter Roberson 2013-4-12

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/71792-solve-seven-nonlinear-equations-with-seven-variables-in-matlab#answer_82024

在 MATLAB Online 中打开

There are two solution sets:

Eo = 7308.837897,
a = -111067.8168,
b = 569105.6911,
e1 = 56.07057628+300.3704267*1i,
e2 = -517.5135254,
t1 = -0.5741854156e-2+0.3075914851e-1*1i,
t2 = 0.9863006784e-1
Eo = 7308.837897,
a = -111067.8168,
b = 569105.6911,
e1 = -517513.5254,
e2 = 0.5607057628e-1+.3003704267*1i,
t1 = 0.9863006784e-1,
t2 = -0.5741854156e-2+0.3075914851e-1*1i

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Walter Roberson 2013-4-12

编辑：Walter Roberson 2013-4-12

在 MATLAB Online 中打开

In Maple, I used

solve(['0.1e-1*Eo+a*0.1e-1^2+b*0.1e-1^3+0.1e-2*t1*e1*(1-exp(-.1/t1))+t2*e2*(1-exp(-.1/t2)) = 30', '0.2e-1*Eo+a*0.2e-1^2+b*0.2e-1^3+0.1e-2*t1*e1*(1-exp(-.2/t1))+t2*e2*(1-exp(-.2/t2)) = 62', '0.3e-1*Eo+a*0.3e-1^2+b*0.3e-1^3+0.1e-2*t1*e1*(1-exp(-.3/t1))+t2*e2*(1-exp(-.3/t2)) = 86', '0.4e-1*Eo+a*0.4e-1^2+b*0.4e-1^3+0.1e-2*t1*e1*(1-exp(-.4/t1))+t2*e2*(1-exp(-.4/t2)) = 101', '0.5e-1*Eo+a*0.5e-1^2+b*0.5e-1^3+0.1e-2*t1*e1*(1-exp(-.5/t1))+t2*e2*(1-exp(-.5/t2)) = 108', '0.6e-1*Eo+a*0.6e-1^2+b*0.6e-1^3+0.1e-2*t1*e1*(1-exp(-.6/t1))+t2*e2*(1-exp(-.6/t2)) = 111', '0.7e-1*Eo+a*0.7e-1^2+b*0.7e-1^3+0.1e-2*t1*e1*(1-exp(-.7/t1))+t2*e2*(1-exp(-.7/t2)) = 111'])

Note: the '' are not needed in Maple and just happen to not hurt either.

Haris Hameed 2013-4-12