Solving implicit equations (variable in summation) without the Symbolic Toolbox

Hi, I am trying to solve implicit equation in the following general form without the Symbolic Toolbox.

n and N are inputs, and the corresponding parameters (Ci, Ki and Cj, Qj) are known. But I need to automate this calculation for different values of n and N based on what I need.

I am struggling with writing the mathematical expression for a series without using a symbol for a variable. There are other solutions for solving implicit equations without Symbolic Toolbox, but I get stuck when I try to generalize them for a series.

Any help would be greatly appreciated.

Thanks, SP

Answer 1

[Sailesh Sidhwani]

Assuming C,K and Q are vectors. You can write your implicit equation as an anonymous function "fun" as follows:

fun = @(x) x + sum((C(1:n)+x) ./ (K(1:n)*x*x)) + sum((C(1:N)*x) ./ (Q(1:N)+x))

Now you can pass this anonymous function "fun" to "fsolve" to solve your implicit equation. You can find the "fsolve" documentation below: https://www.mathworks.com/help/optim/ug/fsolve.html

[Alan Weiss]

You might need to put in some sum expressions to get this to work.

Alan Weiss

MATLAB mathematical toolbox documentation

[Sailesh Sidhwani]

Thanks Alan for pointing that out.