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Numerical Methods for system of integral equations

Konstantin

New member
Aug 26, 2020
1
Are there any standart ways to solve such systems?
\[ \begin{cases} m(t, x) - f(t, x)= \int_{0}^{t} q(\tau,x) \, d\tau \\ u(t,x) = \int_{-\infty}^{+\infty} \frac{1}{2 \sqrt{\pi s t}} e^{-\frac{(x-\xi)^2}{4st}} f(t,x-\xi) \, d\xi \end{cases} \]

Unknown functions are \( f(t,x) \) and \( q(t,x) \), \( t \in [0,T] \), \( s > 0 \).

Can Tikhonov regularization method be used to solve such system?