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Numerical solution of integral equation with parametric variable

11 vues (au cours des 30 derniers jours)
Ann
Ann le 7 Avr 2011
Modifié(e) : Pooyan le 9 Juin 2014
Hello!
Please, how can I solve integral equation in Matlab
L = integral (f(b,t)) dt for third variable (parametric variable b)
Limits of integral are t0, t1.

Réponse acceptée

Jarrod Rivituso
Jarrod Rivituso le 7 Avr 2011
OK, I'm gonna assume you want to do it numerically. Check out this (warning, it gets a little crazy with the function handles):
function solveIntegralForB
bfound = fsolve(@func2minimize,2)
function output = func2minimize(b)
t0 = 0;
t1 = 3;
L = 50;
output = (L - quad(@myFunc,t0,t1))^2;
function f = myFunc(t)
f = exp(b*t);
end
end
end
Essentially, what it does is use the quad function to perform an integration for some value of b. Additionally, it uses the fsolve function to then minimize the "func2minimize" function, which performs the integral for some value of b and checks it against my desired solution.
Here, I've assumed a simple function (exp(b*t)) as f, but you could see how it could be changed. Of course, this is an iterative solution, so there's no guarantee of it finding a solution for all functions f.
Hope this helps!
  1 commentaire
Pooyan
Pooyan le 9 Juin 2014
Modifié(e) : Pooyan le 9 Juin 2014
How if L is a known function of t and b is an unknown function of t? Can anyone help me on that? and again I want to solve the equation for b(t). Let's assume L(t)= sin(t) and t=0:0.1:10;
Thanks.

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Plus de réponses (2)

Matt Tearle
Matt Tearle le 8 Avr 2011
A variation on Jarrod's approach, using function handles (because everyone loves function handles):
myFunc = @(t,b) exp(t*b); % or whatever
t0 = 0;
t1 = 3;
L = 50;
f = @(b) quad(@(t) myFunc(t,b),t0,t1);
bsolve = fzero(f,2);
Or fsolve instead of fzero if you have Optimization Toolbox.

Walter Roberson
Walter Roberson le 11 Avr 2011
If you have the symbolic toolbox,
syms x b
solve(int(f(x,b),x,t0,t1)-L,b)
In theory if it can be solved symbolically it will do so, and if not then MuPad should switch to numeric integrations, I think.

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