How to solve a system of integral equations?

9 visualizaciones (últimos 30 días)
Pavel M
Pavel M el 14 de Feb. de 2020
Comentada: Star Strider el 14 de Feb. de 2020
I want to solve the system of integral equations, but limits on integrals contain an unknown ( x(2) ) which i want to find.
I try this:
function S = Integralsystem(x, t1, t2, n, a, b, Umax1, Umax2);
fun = @(T) x(2) - (Umax1/n)*(exp(a*(T*1e-6)) - exp(b*(T*1e-6)));
t01 = fzero(fun, 0.1);
fun = @(T) x(2) - (Umax2/n)*(exp(a*(T*1e-6)) - exp(b*(T*1e-6)));
t02 = fzero(fun, 1.1);
fun1 = @(T) ((Umax1/n)*(exp(a*(T*1e-6)) - exp(b*(T*1e-6)))) - x(2);
fun2 = @(T) ((Umax1/n)*(exp(a*(T*1e-6)) - exp(b*(T*1e-6)))) - x(2);
S(1) = x(1) - (integral(fun1,t01,t1));
S(2) = x(1) - (integral(fun2,t02,t2));
end
s = fsolve(@(x) Integralsystem(x, t1, t2, n, a, b, Umax1, Umax2),[100 1000])
but Matlab cant find solution.

Respuestas (1)

Star Strider
Star Strider el 14 de Feb. de 2020
It is probably best to use the more robust fsolve in the function instead of fzero.
Try this:
function S = Integralsystem(x, t1, t2, n, a, b, Umax1, Umax2);
fun1 = @(T) x(2) - (Umax1/n)*(exp(a*(T*1e-6)) - exp(b*(T*1e-6)));
t01 = fsolve(fun1, 0.1);
fun2 = @(T) x(2) - (Umax2/n)*(exp(a*(T*1e-6)) - exp(b*(T*1e-6)));
t02 = fsolve(fun2, 1.1);
fun3 = @(T) ((Umax1/n)*(exp(a*(T*1e-6)) - exp(b*(T*1e-6)))) - x(2);
fun4 = @(T) ((Umax1/n)*(exp(a*(T*1e-6)) - exp(b*(T*1e-6)))) - x(2);
S(1) = x(1) - (integral(fun3,t01,t1));
S(2) = x(1) - (integral(fun4,t02,t2));
end
s = fsolve(@(x) Integralsystem(x, t1, t2, n, a, b, Umax1, Umax2),[100 1000])
This slightly revised code (with random scalar values for the other agruments) ran without error and produced a (1x2) vector for ‘s’.
  2 comentarios
Pavel M
Pavel M el 14 de Feb. de 2020
i use fzero because tmin - limit of integral has such condition t0 = f(x(2))
Star Strider
Star Strider el 14 de Feb. de 2020
With the random scalars I supplied to test your function, fzero threw errors. That was the reason I substituted fsolve. Use whatever works best in your application.

Iniciar sesión para comentar.

Categorías

Más información sobre Systems of Nonlinear Equations en Help Center y File Exchange.

Productos


Versión

R2016b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by