passed to equation that has variable of symbolic

I want to get solution of literaion this code by passing equation that has variable of symbolic

syms Z1 Z2 Z3 Za Zc C L 

k=10;

for i = 1:k
    Z11 = 2*Z1 +Z3 == (Za + Zc)^2/(2*(Za+Zc))
    Z21 = Z3 == (Za^2-Zc^2)/(2*(Za+Zc))
    eqn1 = [Z11,Z21];

    [Za, Zc] = solve(eqn1,[Za,Zc])
    %[Za, Zc] = update_var(Za,Zc)
    [Za] = simplify(parallel(Za,C))
    
    Z11 = 2*Z1 +Z3 == (Za + Zc)^2/(2*(Za+Zc))
    Z21 = Z3 == (Za^2-Zc^2)/(2*(Za+Zc))
    eqn2 = [Z11,Z21]
   
    [Z1, Z3] = solve(eqn2,[Z1,Z3])
    [Z1] = simplify(serial1(Z1,L))
    % after solve equation, Z1,Za is overwritten with a expression, sol of equation?
end

Answer 1

[Walter Roberson]

as discussed in https://www.mathworks.com/matlabcentral/answers/570979-second-argument-must-be-a-vector-of-symbolic-variables#answer_471310 your equations as stated cannot be solved. After the first iteration, Z1 is no longer a symbolic variable (it is a symbolic expression instead) and so you cannot solve for it.

[je heo]

Thank you for your answer. then, Is there any way to solve the equation using syms variable??

[Walter Roberson]

I do not know. Maybe you could get something useful with the below. It treats each iteration as having a Z1 and Z3 to be added to the previous Z1 Z3 values.

syms Z2 Za Zc C L 

k=10;

Z1 = syms(Z1, [1 k+1]);
Z3 = syms(Z1, [1, k+1]);

Z1(1) = 0;
Z3(1) = 0;

for i = 1:k
    Z11 = 2*sum(Z1(1:k+1)) + sum(Z3(1:k+1)) == (Za + Zc)^2/(2*(Za+Zc));
    Z21 = sum(Z3(1:k+1)) == (Za^2-Zc^2)/(2*(Za+Zc));
    eqn1 = [Z11,Z21];

    [Za, Zc] = solve(eqn1,[Za,Zc]);
    %[Za, Zc] = update_var(Za,Zc)
    [Za] = simplify(parallel(Za,C));
    
    Z11 = 2*sum(Z1(1:k+1)) + sum(Z3(1:k+1))  == (Za + Zc)^2/(2*(Za+Zc));
    Z21 = sum(Z3(1:k+1)) == (Za^2-Zc^2)/(2*(Za+Zc));
    eqn2 = [Z11,Z21];
   
    [Z1(k+1), Z3(k+1)] = solve(eqn2,[Z1(k+1),Z3(k+1)]);
    [Z1(k+1)] = simplify(serial1(Z1(K+1),L));
end

cumsum(Z1)
cumsum(Z3)

We do not have parallel() or serial1() to test this out with... and we probably would not know if the answer was reasonable or not.