Solving nonlinear equation involving sum

Question

Tiku 2021-6-29

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/868218-solving-nonlinear-equation-involving-sum

评论： Walter Roberson 2021-7-22

Hi,

I am trying to solve a nonlinear equation.

Code

syms g y z n

x = 0.0585;

y = 0.01;

Pi = sym(pi);

eqn = 1/g-sqrt(1 + z.^2/((2*n+1)*Pi*y + 4.4*Pi*x*g).^2) == 0;

sol = solve(eqn, g, 'returnconditions', true, 'maxdegree', 4);

G = simplify(sol.g)

Above gives me four root as suggested in https://www.mathworks.com/matlabcentral/answers/829308-solutions-are-only-valid-under-certain-conditions?s_tid=prof_contriblnk by Walter Robertson.

My code to solve nonlinear equation

sumArg4 = @ (n,z) 2*pi*(2*n+1)*pi*(G(4)-1)/((2*n+1)*pi + 4.4*pi*x/y)/((2*n+1)*pi + 4.4*pi*x*G(4)/y) + 0.6431;

Here only one out of above four roots satisfies so I took fourth roots (have done those calculation in Mathematica)

mytrial4 = @ (z) symsum(sumArg4 , n, 0, 10000)

%Solving nonlinear equation for z

zsol = fsolve(mytrial4, 2.28)

I read some of the posts where they say fsolve can't be used for symbolic expression.

Running above code gave me an error

function_handle with value:

@(z)symsum(sumArg4,n,0,10000)

Error using fsolve (line 309)

FSOLVE requires all values returned by functions to be of data type double.

Error in solveg_new_gz (line 24)

zsol = fsolve(mytrial4, 2.28)

So could you please suggest me how to take care of this error?

I have done in Mathematica but would like to try in Matlab as well.

Thank you

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Answer 1

Ildeberto de los Santos Ruiz 2021-7-21

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https://ww2.mathworks.cn/matlabcentral/answers/868218-solving-nonlinear-equation-involving-sum#answer_751484

在 MATLAB Online 中打开

It will take you a long time to evaluate the sum from n = 0 to n = 10000.

You can solve it in a short time considering only from n = 0 to n = 10, although it is also necessary to define the equation as a numerical function handle.

% ...
mytrial4 = @(z) double(eval(symsum(sumArg4, n, 0, 10)))
zsol = fsolve(mytrial4, 2.28)

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Walter Roberson 2021-7-22

Do not eval() a symbolic expression. The language of symbolic expressions displayed to the user is not MATLAB and is not MuPad (the internal symbol engine). Use subs() if you must.

In some cases you can use matlabFunction to speed up computation.

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