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### Integral equation solver

Hi All,

Is there any way to solve an integral equation, either analytically or numerically?

Thanks,

Daniel Volinski

 2 None slelievre 17654 ●22 ●160 ●348 http://carva.org/samue...

### Integral equation solver

Hi All,

Can Sage solve integral equations

Is there any way to solve an integral equation, (where the unknown is a function and the equation involves integrals), either analytically or numerically?

Thanks,For example, can Sage solve a Volterra equation of the second kind?

Daniel VolinskiThat would be an equation like:

y(x) == integrate(exp(x-t)*y(t), t, 0, x)


and the solution is expected in the form $y(x) = ?$ where the right hand side is a function of $x$ not involving $y$.

 3 None slelievre 17654 ●22 ●160 ●348 http://carva.org/samue...

### Integral equation solver

Can Sage solve integral equations (where the unknown is a function and the equation involves integrals), either analytically or numerically?

For example, can Sage solve a Volterra equation of the second kind?kind?

That would be an equation like:

y(x) == integrate(exp(x-t)*y(t), t, 0, x)


and the solution is expected in the form $y(x) = ?$ where the right hand side is a function of $x$ not involving $y$.

 4 None slelievre 17654 ●22 ●160 ●348 http://carva.org/samue...

### Integral equation solver

Can Sage solve integral equations equations (where the unknown is a function function and the equation involves integrals), integrals), either analytically or numerically?

References:

For example, can Sage solve a Volterra equation of the second kind?

That would be an equation like:, such as

y(x) == integrate(exp(x-t)*y(t), t, 0, x)


and the The solution is expected in the form $y(x) = ?$ ...$where the right hand side is a an explicit function of$x$not involving$y$. Notice in the example the function$y\$ appears in two places, once in the left hand side and the other inside the integral sign.

I am looking for something like what you see in

i.e., a command that would give the solution once I give the equation.