Fredholm Integral Equation - Equation of The Second Kind

Equation of The Second Kind

An inhomogeneous Fredholm equation of the second kind is given as

Given the kernel K(t,s), and the function, the problem is typically to find the function . A standard approach to solving this is to use the resolvent formalism; written as a series, the solution is known as the Liouville-Neumann series.

Read more about this topic:  Fredholm Integral Equation

Famous quotes containing the words equation and/or kind:

    “Jail sentences have many functions, but one is surely to send a message about what our society abhors and what it values. This week, the equation was twofold: female infidelity twice as bad as male abuse, the life of a woman half as valuable as that of a man. The killing of the woman taken in adultery has a long history and survives today in many cultures. One of those is our own.”
    —Anna Quindlen (b. 1952)

    “America is like one of those old-fashioned six-cylinder truck engines that can be missing two sparkplugs and have a broken flywheel and have a crankshaft that’s 5000 millimeters off fitting properly, and two bad ball-bearings, and still runs. We’re in that kind of situation. We can have substantial parts of the population committing suicide, and still run and look fairly good.”
    —Thomas McGuane (b. 1939)