Accelerating convergence of one-step methods for the numerical solution of ordinary differential equations

Abstract

A known result is combined with theorems proved in this paper to show that any one-step method for the numerical solution of the initial value problem

has asympotic error expansion, and to prove an extrapolation theorem on accelerating the convergence of the numerical method.

¹Supported in past by NASA-Manned Spacecraft Center, Houston, Texas under contract NAS 9-3848.

¹Supported in past by NASA-Manned Spacecraft Center, Houston, Texas under contract NAS 9-3848.

Notes

¹Supported in past by NASA-Manned Spacecraft Center, Houston, Texas under contract NAS 9-3848.