how to solve the below transcendental equation for the given data?

format compact
syms T t0 
lambda=600; b=3;
theta=0.02;
c=5;
k=250;
h=1.75;
p=50;
M=.12;
Id=0.003;
TC=(k/T)+(c*lambda)+((lambda*(c*theta+h)*(exp(theta*t0)-theta*t0-1))/(T*(theta)^2))+((lambda*b*(T-t0)^2)/(2*T))+((lambda*p*M^2*Id)/(2*T));
dTCdt0=diff(TC,t0);
dTCdT=diff(TC,T);
[T,t0]=solve(dTCdt0,dTCdT)

Warning: Unable to solve symbolically. Returning a numeric solution using vpasolve.

T = 

0.8526169358775188513228900752894

t0 = 

0.5263315087626859744339029312836

t0=subs(t0);
digits(3)
t0=vpa(t0)

t0 = 

0.526

T=subs(T);
T=vpa(T)

T = 

0.853

TC=subs(TC);
digits(3)
TC=vpa(TC);
TC=round(TC)

TC = 

3587

%z=sqrt((2*k*(h+c*theta)*b)/(b+h+(c*theta)))*(sqrt(3800)-137.816)

[M.Rameswari Sudha]

If I run the above code new file, I got the answer. Again If I run, i will get the below comments.

T =

Empty sym: 0-by-1

t0 =

[]

t0 =

[ empty sym ]

T =

Empty sym: 0-by-1

TC =Warning: Unable to display symbolic object because 'symengine' was reset. Repeat commands to regenerate result. > In sym/disp (line 59)

In sym/display>displayVariable (line 97)

In sym/display (line 58)

In PRABACASE11 (line 26)

[Manikanta Aditya]

Hi @M.Rameswari Sudha,

The issue you're facing with the code not working consistently is likely due to the symbolic engine being reset or cleared between runs. This can happen if you're running the code in different sessions or if some other operation clears the symbolic engine's state.

To ensure consistent behavior, you could try encapsulating the entire code in a function and calling that function each time you want to execute it. This way, the symbolic engine's state is reset at the beginning of each function call.

Here's an example of how you could structure the code as a function:

function [T, t0, TC] = solve_transcendental_equation()
    syms T t0

    lambda = 600; b = 3;
    theta = 0.02;
    c = 5;
    k = 250;
    h = 1.75;
    p = 50;
    M = 0.12;
    Id = 0.003;

    TC = (k/T) + (c*lambda) + ((lambda*(c*theta+h)*(exp(theta*t0)-theta*t0-1))/(T*(theta)^2)) + ((lambda*b*(T-t0)^2)/(2*T)) + ((lambda*p*M^2*Id)/(2*T));

    dTCdt0 = diff(TC, t0);
    dTCdT = diff(TC, T);

    [T_sol, t0_sol] = vpasolve(dTCdt0, dTCdT, [T, t0]);

    T = double(T_sol);
    t0 = double(t0_sol);

    TC = subs(TC);
    digits(3);
    TC = vpa(TC);
    TC = round(TC);
end

You can then call this function as many times as you need, and it should provide consistent results:

[T, t0, TC] = solve_transcendental_equation()

I hope this helps, if this helps, let me know I will post as answer, you can accept it to make it more helpful.

[M.Rameswari Sudha]

Hi@Manikanta Aditya,

Thank you. Now, I understand the mistake. I got the answer.

Answer 1

[Manikanta Aditya]

Hi,

The issue you're facing with the code not working consistently is likely due to the symbolic engine being reset or cleared between runs. This can happen if you're running the code in different sessions or if some other operation clears the symbolic engine's state.

To ensure consistent behavior, you could try encapsulating the entire code in a function and calling that function each time you want to execute it. This way, the symbolic engine's state is reset at the beginning of each function call.

Here's an example of how you could structure the code as a function:

function [T, t0, TC] = solve_transcendental_equation()
syms T t0
lambda = 600; b = 3;
theta = 0.02;
c = 5;
k = 250;
h = 1.75;
p = 50;
M = 0.12;
Id = 0.003;
TC = (k/T) + (c*lambda) + ((lambda*(c*theta+h)*(exp(theta*t0)-theta*t0-1))/(T*(theta)^2)) + ((lambda*b*(T-t0)^2)/(2*T)) + ((lambda*p*M^2*Id)/(2*T));
dTCdt0 = diff(TC, t0);
dTCdT = diff(TC, T);
[T_sol, t0_sol] = vpasolve(dTCdt0, dTCdT, [T, t0]);
T = double(T_sol);
t0 = double(t0_sol);
TC = subs(TC);
digits(3);
TC = vpa(TC);
TC = round(TC);
end

You can then call this function as many times as you need, and it should provide consistent results:

[T, t0, TC] = solve_transcendental_equation()

I hope this helps, if this helps, let me know I will post as answer, you can accept it to make it more helpful.