Moving averages of ordinary differential equations via convolution
The averaging method of ordinary differential equations approximates the solution of a time-varying system with a small amplitude on a long time domain, by the solution of an auxiliary time-invariant system. The paper establishes a different approach to the averaging method that works under conditions that are not covered by the standard method, for instance, the existence of the time average is not required. Namely, the paper introduces an averaging framework, where the solution of a time-varying equation with 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 a smoothing of the equation, thus, making it more amenable to numerical computations. Results on the approximation error for general classes of vector fields and kernels are presented.
averaging method of ordinary differential equations
scientific article; zbMATH DE number 5836850