A fast algorithm for convolution integrals with space and time variant kernels

Mathematical models in many fields of the physical sciences involve nonlocal terms which are formally similar to convolution integrals. We show that it is possible to approximate a particular class of such integrals, which by themselves are not convolutions, as a linear combination of convolution integrals, allowing for their efficient numerical computation as an O(NlogN)O(NlogN) process.