On the numerical stability of the exponentially fitted methods for first order IVPs

摘要

In the numerical solution of Initial Value Problems (IVPs) for differential systems, exponential fitting (EF) techniques are introduced to improve the accuracy behaviour of classical methods when some information on the solutions is known in advance. Typically, these EF methods are evaluated by computing their accuracy for some test problems and it is usual to assume that the stability behaviour is similar to the underlying classical methods. The aim of this paper it to show that for some standard methods the stability behaviour of their exponentially fitted versions may change strongly. Furthermore, this stability depends on the choice of the fitting space, that must be carefully selected in order to assess the quality of the integrators for the IVPs under consideration. In particular, we will show that for the usual fitting space 〈exp(ωx),exp(−ωx)〉 with ω∈R the size of the stability domain of the EF method can be much smaller than the one for the original method.