The solution process takes too long+vpasolve

Pooneh Shah Malekpoor

2020 7 10

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Hello, I am solving a single variable nonlinear equation(i.e. eqn) using vpasolve. The solution speed is fine if n is equal to 10. However, it gets (kind of) stuck when I increase the n to 20. What is your recommendation?

*P.S. This code is a part of a major code in which C, l, beta, A, rho and... are all defined.

tol=0.001;
Error=100;
te=0;
 EE=sym(zeros(n+1,1));
while Error>tol
 syms x positive
for i=1:n+1
    if i==1
        EE(1,1)=0;
    
    else
    EE(i,1)=(((C*l(i-1)/x)+(((tan(phi*pi/180))/x)*((rho*9.81*A(i-1)*(cos(beta(i-1))))+(EE(i-1)*(sin(beta(i-1)-(te))))))-(rho*9.81*A(i-1)*(sin(beta(i-1))))+(EE(i-1)*(cos(beta(i-1)-(te)))))/((cos(beta(i-1)-(te)))+((sin(beta(i-1)-(te)))*(tan(phi*pi/180))/x)));
    
     end
end
eqn = (simplify((EE(n+1,1))));
[k] =max(vpasolve(eqn, x ,[0.1 5]));

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John D'Errico 2020-7-10

Recommendation(s)?

Don't indcrease n to 20.
Get a bigger, faster computer.

As you increase n, at each iteration, each step uses the result from the previous step in the loop.

You don't tell us what all of those unknown constants are, so I cannot really do too much. But remember that EE is getting bigger, nastier, messier, at each and every step. So what do you expect?

Pooneh Shah Malekpoor 2020-7-10

My analyses is such that I should compare the results also for n=20. so, the results for n=20 is as important as when n=10.

My question is, Does vpasolve, fsolve and fzero have the same speed when solving such an equation?

I should say again that C,phi and rho are constants and all A, beta, l are coded based on geometrical coordinates. The main problem (as you mentioned) in this nonlinear equation is that there are EE on both sides.

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