Exponential time differencing for stiff systems

We develop a class of numberical methods for stiff systems, exponential time differencing. We describe schemes with second- and higher-order accuracy, introduce new Runge-Kutta versions of these schemes, and extend the method to show how it may be applied to systems whose linear part is nondiagonal. We test the method against other common schemes, including integrating factor and linearly implicit methods, and show how it is more accurate in a number of applications We apply the method to both dissipative and partial differential equation, after illustrating its behavior using, forced ordinary differential equations with stiff linear parts. (C) 2002 Elsevier Science (USA).