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
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
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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