Summation equation

In mathematics, a summation equation or discrete integral equation is an equation in which an unknown function appears under a summation sign. The theories of summation equations and integral equations can be unified as integral equations on time scales[1] using time scale calculus. A summation equation compares to a difference equation as an integral equation compares to a differential equation.

The Volterra summation equation is:

x(t) = f(t) + \sum_{i=m}^n k(t, s, x(s))

where x is the unknown function, and s, a, t are integers, and f, k are known functions.

References

  1. ↑ Volterra integral equations on time scales: Basic qualitative and quantitative results with applications to initial value problems on unbounded domains, Tomasia Kulik, Christopher C. Tisdell, September 3, 2007