Abstract In numerical simulations of complex flows with discontinuities, it is necessary to use nonlinear schemes. The spectrum the scheme used has a significant impact on resolution and stability computation. Based approximate dispersion relation method, we combine corresponding spectral property preservation proposed by De Eswaran (J Comput Phys 218:398–416, 2006) propose quasi-linear (QL-GRP...

We extend a recent asymptotic normality theorem for generalized linear mixed models to include the dispersion parameter. The maximum likelihood estimators of all model parameters have asymptotically normal distributions with mutual independence between fixed effects, covariance and parameters.