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Numerical solution of integral equation with parametric variable

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Ann
Ann 2011-4-7
编辑： Pooyan 2014-6-9
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.

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Jarrod Rivituso
Jarrod Rivituso 2011-4-7
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 个评论
Pooyan
Pooyan 2014-6-9
编辑：Pooyan 2014-6-9
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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更多回答（2 个）

Matt Tearle
Matt Tearle 2011-4-8
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 2011-4-11
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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