How to find roots of an implicit exprerssion

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Uday 2015-7-22

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https://ww2.mathworks.cn/matlabcentral/answers/230746-how-to-find-roots-of-an-implicit-exprerssion

编辑： Walter Roberson 2015-7-23

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Can anyone please tell me how to find roots of the following expression in MATLAB (solve for k) :

f(k) = -U + X/t(i) + (h*k*sech (k*h)^2 + tanh (k*h))/(2*(k*tanh (k*h))^(1/2));

for

U = 1; 
X = 100; 
h = 10; 
t = 210:300 ?

Thank you in advance

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Torsten 2015-7-22

Try MATLAB's "solve".

If no explicit solution can be found, use MATLAB's "fzero" for the function

func(k)=f(i)-(-U + X/t(i) + (h*k*sech (k*h)^2 + tanh (k*h))/(2*(k*tanh (k*h))^(1/2)))

Best wishes

Torsten.

Walter Roberson 2015-7-23

编辑：Walter Roberson 2015-7-23

Could you confirm that you know the value of f(k) and you are solving for the k that makes the left hand side equal the right hand side? Or are you looking for the k that makes the right hand side zero?

If you are looking for the k that makes the right hand side zero, then my tests show me that the value will be slightly less than 1 for t(n) = 210, and will decrease as t(n) increases, declining to about .56 at t(n) = 300.

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