A stable semi-implicit algorithm
arXiv:1905.04520
Abstract
When the singular values of the evolution operator are all smaller or all greater than one, stable integration algorithms are obtained either by explicit or implicit methods. When the singular spectrum mixes greater and smaller than one values, neither explicit nor implicit methods insure stabilty. The problem is solved by using a splitting of the evolution operator and a semi-implicit scheme. The method is illustrated in the study of a two-field model of the tokamak scrape-off layer.
Although the matrix decomposition results are correct, they are only applicable to the integration of differential systems when the decomposition matrices M_1 and M_2 are of order δ_t