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 scales¹ 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: $x(t)=f(t)+\sum _{s=m}^{n}k{\bigl (}t,s,x(s){\bigr )}$ where $x$ is the unknown function, $s, t$ are integers, and $f, k$ are known functions.

References

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

Summation equations or discrete integral equations

[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

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