People who write software have probably looked at numerical integration like Simpson’s rule or the midpoint rule. That makes it pretty obvious that integration is summing up small bits of something.

Backward error analysis has become an important tool for understanding the long time behavior of numerical integration methods. This is true in particular for the integration of Hamiltonian systems ...

The numerical solution of wave scattering from large objects or from a large cluster of scatterers requires excessive computational resources and it becomes necessary to use approximate-but ...