Increasing the order of accuracy for the evolutionary variable of the compact difference schemes approximating the equations of nonlinear fiber optics
The compact finite difference scheme for the equations of nonlinear fiber optics developed by the authors earlier has the second order of approximation with respect to the evolutionary variable so the problem for the improvement of approximation accuracy without essential complication of the scheme is still open. Considering the study of this issue as a goal, we applied parametric averaging and formulated conditions under which the approximation order increases. It is proved that in case of the symmetric averaging the order of approximation increases to the fourth order; however the scheme becomes absolutely unstable. In case of the asymmetrical averaging it is possible to construct schemes of the third order of approximation, however the condition of their stability is so strong that there are no advantages compared to the earlier schemes developed by the authors.