Asymptotic analysis of singularly perturbed systems of ordinary differential equations

AbstractPresented in this paper is a new algorithm for the asymptotic expansion of a solution to an initial value problem for singularly perturbed (stiff) systems of ordinary differential equations. This algorithm is related to the Chapman-Enskog asymptotic expansion method used in the kinetic theory to derive the equations of hydrodynamics, whereas the standard algorithm pertains to the Hilbert approach known to give inferior results. In cases of systems of ordinary differential equations the new algorithm leads to the reduction of numerical effort needed to achieve a given accuracy as compared with the standard asymptotic expansion method. The proof of the asymptotic convergence is given. The numerical example demonstrates the feasibility of the new approach