wrong solutions in system of nonlinear equations with "vpasolve"

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Naohiro Kato
Naohiro Kato 2020-10-14
评论： Naohiro Kato 2020-10-22
Hello, I am a beginner of Matlab.
I tried to solve a system of nonlinear equations (8 equation and 6 variables) with vpasolve as shown below.
The solutions do not satisfy 4 out of 8 equations. (Wrong solutions and equations that are not satisfied with the solutions are with bold letters.)
How can I fix the problem?
*Code I used
//
>> syms A B C D E x
eq1=B+C+7.5-100
eq2=A+C+E+7.5-135
eq3=D+E+7.5-15
eq4=0.7*C + x*E - A*(B+D)
eq5=0.7*(C+7.5)-B*(A+E)
eq6=0.7*C-x*7.5-(A*B-C*D)
eq7=x*(E+7.5)-D*(A+C)
eq8=x*E-0.7*7.5-(A*D-B*E)
eqs=[eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8]
[A, B, C, D, E, x]=vpasolve(eqs, [A,B,C, D, E, x])
//
*Response I got
//
eq1 = B + C - 185/2
eq2 = A + C + E - 255/2
eq3 = D + E - 15/2
eq4 = (7*C)/10 + E*x - A*(B + D)
eq5 = (7*C)/10 - B*(A + E) + 21/4
eq6 = (7*C)/10 - (15*x)/2 - A*B + C*D
eq7 = x*(E + 15/2) - D*(A + C)
eq8 = E*x - A*D + B*E - 21/4
eqs = [ B + C - 185/2, A + C + E - 255/2, D + E - 15/2, (7*C)/10 + E*x - A*(B + D), (7*C)/10 - B*(A + E) + 21/4, (7*C)/10 - (15*x)/2 - A*B + C*D, x*(E + 15/2) - D*(A + C), E*x - A*D + B*E - 21/4]
A =
34.046247300863523845963342329846
29.073162677776520552338619357279
-2.4237473008635238459633423298465
-6.8461164144313248228012528092361
B =
1.8635105955281338875279376538881
1.8635105955281338875279376538881
-37.563510595528133887527937653888
-37.563510595528133887527937653888
C =
90.636489404471866112472062346112
90.636489404471866112472062346112
130.06351059552813388752793765389
130.06351059552813388752793765389
D =
4.6827367053353899584354046759584
-0.29034791775161333518931829660926
7.6397632946646100415645953240416
3.217394181096809064726684844652
E =
2.8172632946646100415645953240416
7.7903479177516133351893182966093
-0.13976329466461004156459532404161
4.282605818903190935273315155348
x =
56.590242103608342266508720016265
-2.2731626777765205523386193572788
132.48725789639165773349127998373
33.646116414431324822801252809236
//

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回答（1 个）

Nagasai Bharat
Nagasai Bharat 2020-10-20
Hi,
There is an syntax error in how the "vpasolve" function is being solved. Do look in the below snippet for correct syntax.
Refer vpasolve mathwork documentaton for more detail.
syms A B C D E x
eq1=B+C+7.5-100;
eq2=A+C+E+7.5-135;
eq3=D+E+7.5-15;
eq4=0.7*C + x*E - A*(B+D);
eq5=0.7*(C+7.5)-B*(A+E);
eq6=0.7*C-x*7.5-(A*B-C*D);
eq7=x*(E+7.5)-D*(A+C);
eq8=x*E-0.7*7.5-(A*D-B*E);
[A, B, C, D, E, x]= vpasolve(eq1 == 0, eq2 == 0, eq3 == 0, eq4== 0, eq5== 0, eq6== 0, eq7== 0, eq8== 0, [A,B,C, D, E, x])
  1 个评论
Naohiro Kato
Naohiro Kato 2020-10-22
Deaar Nagasai,
Thak you very much for youre answer.
There seem to be several different syntax to run vpaaslove. I found the syntax you described would give exact same solutions as the syntax I used.
On the other hand, I now noticed that all answers of the equations are 0 or nearly 0 (<+1.2 E-12) when I plug the solutions back into the equations. I simply upset when I saw the solutions are non zero, assuming vpasolve would always give the perect solution of 0.
Thak you again for your help anyway. I keep learnng Matlab.

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