It is the purpose of this paper to derive diagonally implicit exponentially fitted methods for the numerical solution of initial value problems based on first order ordinary differential equations. The approach used takes into account the contribution to the error originated from the computation of the internal stages approximations. The derived methods are then compared to those obtained by neglecting the contribution of the error associated to the internal stages, as classically done in the classical derivation of multistage EF-based methods (compare  and references therein). Standard and revised EF methods are then compared in terms of linear stability and numerical performances.
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