An efficient algorithm for the evaluation of convolution integrals

We propose an algorithm for the numerical evaluation of convolution integrals of the form ∫0xk(x−y)f(y,x) dy, for x [0,X]. Our method is especially suitable in situations where the fundamental interval [0, X] is very long and the kernel function k is expensive to calculate. Separate versions are provided where the forcing function f is known in advance, and where it must be determined step-by-step along the solution path. These methods are efficient with respect to both run time and memory requirements.