# Question:Solving set of non-linear equations

## Question:Solving set of non-linear equations

Maple

Dear All

How do I solve the followinh set of non-linear equations for the unknowns as given below:

Zth1=R1(1-e^(-t1/tau1))+R2(1-e^(-t1/tau2))+R3(1-e^(-t1/tau3))+R4(1-e^(-t1/tau4))+R5(1-e^(-t1/tau5))+R6(1-e^(-t1/tau6))

Zth2=R1(1-e^(-t2/tau1))+R2(1-e^(-t2/tau2))+R3(1-e^(-t2/tau3))+R4(1-e^(-t2/tau4))+R5(1-e^(-t2/tau5))+R6(1-e^(-t2/tau6))

Zth3=R1(1-e^(-t3/tau1))+R2(1-e^(-t3/tau2))+R3(1-e^(-t3/tau3))+R4(1-e^(-t3/tau4))+R5(1-e^(-t3/tau5))+R6(1-e^(-t3/tau6))

Zth4=R1(1-e^(-t4/tau1))+R2(1-e^(-t4/tau2))+R3(1-e^(-t4/tau3))+R4(1-e^(-t4/tau4))+R5(1-e^(-t4/tau5))+R6(1-e^(-t4/tau6))

Zth5=R1(1-e^(-t5/tau1))+R2(1-e^(-t5/tau2))+R3(1-e^(-t5/tau3))+R4(1-e^(-t5/tau4))+R5(1-e^(-t5/tau5))+R6(1-e^(-t5/tau6))

Zth6=R1(1-e^(-t6/tau1))+R2(1-e^(-t6/tau2))+R3(1-e^(-t6/tau3))+R4(1-e^(-t6/tau4))+R5(1-e^(-t6/tau5))+R6(1-e^(-t6/tau6))

Zth7=R1(1-e^(-t7/tau1))+R2(1-e^(-t7/tau2))+R3(1-e^(-t7/tau3))+R4(1-e^(-t7/tau4))+R5(1-e^(-t7/tau5))+R6(1-e^(-t7/tau6))

Zth8=R1(1-e^(-t8/tau1))+R2(1-e^(-t8/tau2))+R3(1-e^(-t8/tau3))+R4(1-e^(-t8/tau4))+R5(1-e^(-t8/tau5))+R6(1-e^(-t8/tau6))

Zth9=R1(1-e^(-t9/tau1))+R2(1-e^(-t9/tau2))+R3(1-e^(-t9/tau3))+R4(1-e^(-t9/tau4))+R5(1-e^(-t9/tau5))+R6(1-e^(-t9/tau6))

Zth10=R1(1-e^(-t10/tau1))+R2(1-e^(-t10/tau2))+R3(1-e^(-t10/tau3))+R4(1-e^(-t10/tau4))+R5(1-e^(-t10/tau5))+R6(1-e^(-t10/tau6))

Zth11=R1(1-e^(-t11/tau1))+R2(1-e^(-t11/tau2))+R3(1-e^(-t11/tau3))+R4(1-e^(-t11/tau4))+R5(1-e^(-t11/tau5))+R6(1-e^(-t11/tau6))

Zth12=R1(1-e^(-t12/tau1))+R2(1-e^(-t12/tau2))+R3(1-e^(-t12/tau3))+R4(1-e^(-t12/tau4))+R5(1-e^(-t12/tau5))+R6(1-e^(-t12/tau6))

RT=R1+R2+R3+R4+R5+R6

How would one solve above system of equations for:

R1, R2, R3, R4, R5, R6, tau1, tau2, tau3, tau4, tau5, tau6

Given:

RT = 0.5
Zth1 = 0.01219
Zth2 = 0.019409
Zth3 = 0.025586
Zth4 = 0.030061
Zth5 = 0.035156
Zth6 = 0.059156
Zth7 = 0.091201
Zth8 = 0.242103
Zth9 = 0.390841
Zth10 =0.461318
Zth11 =0.496592
Zth12 =0.496592
t1 = 19.96e-6
t2 = 50.12e-6
t3 = 100e-6
t4 = 144.54e-6
t5 = 199.53e-6
t6 = 501.19e-6
t7 = 1000e-6
t8 = 10000e-6
t9 = 50118.72e-6
t10 =0.1
t11 =0.5012
t12 =1.0

Regards

ik

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