Summation equation explained

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

References

1. http://web.maths.unsw.edu.au/~cct/tis-tomasia-IJDE-rev.pdf Volterra integral equations on time scales: Basic qualitative and quantitative results with applications to initial value problems on unbounded domains

• Summation equations or discrete integral equations