Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I came across an integral equation of the Form

[tex]x(t)=\int_\mathbb{R_+}{ds\, x(s)K(s,t)}[/tex]

wher K is some real function. (x is also real). Actually I will later need the higher dimensional case

[tex]x(t_1,\dots,t_n)=\int_\mathbb{R_+^n}{ds_1,\dots,ds_n\, x(s_1,\dots,s_n)K(s_1,\dots,s_n,t_1,\dots,t_n)}[/tex]

But it might be good to first learn the one dimensional case.

From my functional analysis course I remember integral equations of the form (of the Volterra type - ah memory comes back)

[tex]x(t)=\int_{-\infty}^t{ds\, x(s)K(s,t)}[/tex]

and I could transform this type on integral equation to the type I mentioned above (integration over R) via indicator functions which could then be absorbed into the kernel function K .... However I don't see how to do this the other way around.

I suppose there is plenty of literature on this kind of equations and I would appreciate it if you could point me to a particularly useful resource or provide some direct explanations and information on the methods to solve such equations

Thanks

-Pere

edit:

I should have looked on Wikipedia first......sorry .... seems to be a homogeneous Fredholm equation of the second kind .....

So there seem to be a couple of solving methods available like Integral Equation Neumann Series, Fourier Transformation ... I will see if something works for me, if not, I'll be back with the explicit formula of the kernel function

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Integral equation

Loading...

Similar Threads - Integral equation | Date |
---|---|

I Equality of two particular solutions of 2nd order linear ODE | Nov 25, 2017 |

A Integral equations -- Picard method of succesive approximation | Nov 14, 2017 |

I Solving this integral equation | Nov 3, 2017 |

I Fredholm integral equation with separable kernel | Jul 9, 2017 |

I Integrating both sides of an equation question | Feb 16, 2017 |

**Physics Forums - The Fusion of Science and Community**