Limiting form of exponential time differencing schemes

Abstract

The problem of finding a stable numerical scheme that handles stiff ordinary differential equations has been around for decades and several methods of solution have been developed over the years. The Exponential Time Differencing (ETD) developed by Cox and Matthew (2002) is one of the best schemes developed ever, though it is yet to receive a wide appreciation. The purpose of this paper is to show that the Exponential Time Differencing Schemes of orders 1, 2, 3 and 4 can be modified and simplified to Adams Bashforth Schemes of the corresponding orders as the stiff coefficients gets smaller.