MATLAB: Solving/plotting a nonlinear equation for multiple values

fsolvefunctionnonlinear equationsthermodynamics

Hello all,
I am a mechanical engineering student working on some Applied Thermodynamics homework and am having trouble getting the values I need to plot a nonlinear equation. I have (on paper) determined that my nonlinear equation is as follow:
2*sqrt(P)*((x)^1.5) + .10905*x- 0.0363 = 0
where P is a pressure and x happens to be a molecular concentration in this case. So, I can solve the above equation for set values of P using the following function file (when P = 1).
function [x,P] = myfun(x)
F = 2*sqrt(1)*((x)^1.5) + .10905*x- 0.03635;
end
and the commands:
x0 = 0.5;
[x,fval] = fsolve(@myfun,x0)
But what I want is to define P as an array like [0.1:0.1:100] and be able to solve all of those values at once instead of having to get each one individually. I was wondering if this was possible using the above approach or if I should be looking at another method. Thank you in advance for any guidance you can give me. Still kind of a Matlab novice if you couldn't already tell.

Best Answer

There are three solutions, two of which are only real-valued between P = 0 and P = 0.000132 (approximately). The third is real-valued for larger P as well.
The order of floating point calculations can make a big difference in functions such as these, sometimes changing the calculations completely. I have therefore converted the floating point values you gave into rational values; the below is in rational
((1/40000)*((581600000000*P^2 - 384240583*P + 29080000*(400000000*P - 528529)^(1/2) * P^(3/2))/P^(5/2))^(1/3) + (528529/40000) / (P*((581600000000*P^2 - 384240583*P + 29080000*(400000000*P - 528529)^(1/2)*P^(3/2)) / P^(5/2))^(1/3)) - (727/40000) / P^(1/2))^2
 (1/4652800000000)*727^(1/3)*((-1+I*3^(1/2))*P^(3/2)*727^(2/3) * ((800000000*P^2 - 528529*P + 40000*(400000000*P - 528529)^(1/2) * P^(3/2)) / P^(5/2))^(2/3) - 1454*P*727^(1/3)*((800000000*P^2 - 528529*P + 40000*(400000000*P - 528529)^(1/2)*P^(3/2)) / P^(5/2))^(1/3) - 528529*(1+I*3^(1/2))*P^(1/2))^2 / (((800000000*P^2 - 528529*P + 40000*(400000000*P - 528529)^(1/2)*P^(3/2))/P^(5/2))^(2/3)*P^3)
 (1/4652800000000)*((1+I*3^(1/2))*P^(3/2)*727^(2/3) * ((800000000*P^2 - 528529*P + 40000*(400000000*P - 528529)^(1/2)*P^(3/2))/P^(5/2))^(2/3) + 1454*P*727^(1/3)*((800000000*P^2 - 528529*P + 40000*(400000000*P - 528529)^(1/2)*P^(3/2)) / P^(5/2))^(1/3) - 528529*P^(1/2)*(-1+I*3^(1/2)))^2*727^(1/3) / (((800000000*P^2 - 528529*P + 40000*(400000000*P - 528529)^(1/2)*P^(3/2)) / P^(5/2))^(2/3)*P^3)
Related Question