RESUMEN
In this paper, an implicit finite difference scheme with the shifted Grünwald formula, which is unconditionally stable, is used to discretize the fractional diffusion equations with constant diffusion coefficients. The coefficient matrix possesses the Toeplitz structure and the fast Toeplitz matrix-vector product can be utilized to reduce the computational complexity from [Formula: see text] to [Formula: see text], where N is the number of grid points. Two preconditioned iterative methods, named bi-conjugate gradient method for Toeplitz matrix and bi-conjugate residual method for Toeplitz matrix, are proposed to solve the relevant discretized systems. Finally, numerical experiments are reported to show the effectiveness of our preconditioners.
RESUMEN
The mutagenic effects of microwave and chromium trioxide (CrO(3)) on Vicia faba root tip were studied. Micronucleus assay and chromosomal aberration assay were used to determine the mitotic index, the micronucleus frequency and chromosomal aberration frequency of Vicia faba root tip cells induced by microwave and CrO(3). The results showed that the micronucleus frequency decreased, and that the mitotic index and chromosomal aberration frequency showed linear dose responses to CrO(3), in treatment of microwave for 5 s. In microwave of 25 s, the mitotic index decreased, the micronucleus frequency and chromosomal aberration frequency increased with increase of CrO(3) concentration. We concluded that microwave and CrO(3) had antagonistic effect on the mitotic index of Vicia faba root tip cells, but had synergetic effect on micronucleus frequency and chromosomal aberration frequency of Vicia faba root tip cells.
