can't solve an equation

Hello,

I'm trying to solve this equation:

Fun=@(T) 1-exp(-n.*S.*( integral(@(T) exp(-E./(k.*T)),Ti,T)) ) ;

Where E=1; k=8.6e-5; n=10; S=1e12; Ti=300;

For T=300:500, this function changes from Fun= [0:1]. So, this function has real values from 0 to 1 in this range of T. However, the matlab can solve this equation for only the values in the range of [0:0.49]. If, for example, Fun=0.5 or 0.6....0.99, the MATLAB gives: "Warning: Explicit solution could not be found."

Here is the details of my code:

The solution of the integral in the equation is given by:

(T.*exp(-E./(k.*T))- ( (E./k).*expint(E./(k.*T)) )) - (Ti.*exp(-E./(k.*Ti))- ( (E./k).*expint(E./(k.*Ti)) ))

So, the final form of the equation will be given as:

fun=1-exp(-n.*S.*( ((T.*exp(-E./(k.*T))- ( (E./k).*expint(E./(k.*T)) )) - (Ti.*exp(-E./(k.*Ti))- ( (E./k).*expint(E./(k.*Ti)) ))))) ;

Examples:

syms T

>> solve(fun==0.2)

ans =

345.05417496592632071516378454629

However,

solve(fun==0.5)

Warning: Explicit solution could not be found.

> In solve at 179

ans =

[ empty sym ]

can anyone help me in this?

Thank you

Answer 1

[SK]

Maybe you need to specify a rough domain where the solution lies or a starting point for the iteration? The solver may not be looking at high enough values of T and so gets stuck at the halfway inflexion point. You may need to ask it to look at the entire interval say 0 to 500. I don't see an option in Matlab to do this but the docs say that you can do it in the Mupad notebook.

Answer 2

[Amr Sadek]

Thank you for your answer

I used the vpasolve built-in function instead of the "solve" function. This function allows me to use start point or searching region for the solution. I tested it and it worked very well.

Thank you.

[SK]

welcome :)