Symmetric embedded predictor~5-corrector (EP~5CM) full in phase methods

摘要

An embedded predictor5-corrector scheme is presented in this paper. The meaning of the terminology predictor~5 is five layers of prediction. We symbolize the new embedded algorithm as (EP~5CM). For the scheme (EP~5CM), the coefficients are determined in order the algorithm to have vanished the phase-lag and its derivatives of the highest possible order for each layer. The linear symmetric ten-step method of Quinlan-Tremaine [1] is used as the first layer (predictor) of the new introduced scheme. The new method can be applied on the approximate solution of: (i) special initial-value problems (IVPs) with oscillating and/or periodical solution, (ii) boundary-value problems (BVPs) with oscillating and/or periodical solution, (iii) orbital problems and (iv) the Schr?dinger equation and related problems. The numerical and theoretical achievements show the efficiency of the new introduced algorithms.