Moving averages of ordinary differential equations via convolution

We introduce an averaging framework, where the solution of a time-varying equation with a small amplitude is approximated by the solution of a slowly-varying auxiliary system, generated by convolving the original equation with a kernel function. The effect of the convolution is smoothing of the equation, thus, making it more amenable to numerical computations. We present tight results on the approximation error for general classes of vector fields and kernels.