Obrechkoff versus super-implicit methods for the solution of first- and second-order initial value problems

AbstractThis paper discusses the numerical solution of first-order initial value problems and a special class of second-order ones (those not containing first derivative). Two classes of methods are discussed, super-implicit and Obrechkoff. We will show equivalence of super-implicit and Obrechkoff schemes. The advantage of Obrechkoff methods is that they are high-order one-step methods and thus will not require additional starting values. On the other hand, they will require higher derivatives of the right-hand side. In case the right-hand side is complex, we may prefer super-implicit methods. The disadvantage of super-implicit methods is that they, in general, have a larger error constant. To get the same error constant we require one or more extra future values. We can use these extra values to increase the order of the method instead of decreasing the error constant. One numerical example shows that the super-implicit methods are more accurate than the Obrechkoff schemes of the same order

Analisis Penggunaan Sarana dan Prasarana untuk Menunjang Kegiatan Belajar Mahasiswa di Universitas PGRI Palembang Tahun Akademik 2016/2017

The benefits of educational facilities greatly affect the smoothness and sustainability of the learning process. Universitas PGRI Palembang has good facilities and infrastructure ranging from comfortable lecture room and has been completed by infocus, accredited library A and integrated lab, and other facilities that support the student learning process, but sometimes facilities that have been maximally completed by University is not in good use by students or by lecturers. This research aimed at investigating the value of benefit from the use of facilities and infrastructure to support the student learning activities in academic year 2016/2017. This research was descriptive by using quantitative approach. The result concluded that the infrastructure facilities in Universitas PGRI Palembang in good categories which were seen from the number of student statement 80,20

Do broad absorption line quasars live in different environments from ordinary quasars?

We select a sample of $\sim 4200$ traditionally defined broad absorption line quasars (BALQs) from the Fifth Data Release quasar catalog of the Sloan Digital Sky Survey. For a statistically homogeneous quasar sample with $1.7\le z\le 4.2$, the BAL quasar fraction is $\sim 14$ and is almost constant with redshift. We measure the auto-correlation of non-BAL quasars (nonBALQs) and the cross-correlation of BALQs with nonBALQs using this statistically homogeneous sample, both in redshift space and using the projected correlation function. We find no significant difference between the clustering strengths of BALQs and nonBALQs. Assuming a power-law model for the real space correlation function $\xi(r)=(r/r_0)^{-1.8}$, the correlation length for nonBALQs is $r_0=7.6\pm 0.8 h^{-1}{\rm Mpc}$; for BALQs, the cross-correlation length is $r_0=7.4\pm 1.1 h^{-1}{\rm Mpc}$. Our clustering results suggest that BALQs live in similar large-scale environments as do nonBALQs.Comment: accepted for publication in Ap

Cluster Alignments and Ellipticities in LCDM Cosmology

The ellipticities and alignments of clusters of galaxies, and their evolution with redshift, are examined in the context of a Lambda-dominated cold dark matter cosmology. We use a large-scale, high-resolution N-body simulation to model the matter distribution in a light cone containing ~10^6 clusters out to redshifts of z=3. Cluster ellipticities are determined as a function of mass, radius, and redshift, both in 3D and in projection. We find strong cluster ellipticities: the mean ellipticity increases with redshift from 0.3 at z=0 to 0.5 at z=3, for both 3D and 2D ellipticities; the evolution is well-fit by e=0.33+0.05z. The ellipticities increase with cluster mass and with cluster radius; the main cluster body is more elliptical than the cluster cores, but the increase of ellipticities with redshift is preserved. Using the fitted cluster ellipsoids, we determine the alignment of clusters as a function of their separation. We find strong alignment of clusters for separations <100 Mpc/h; the alignment increases with decreasing separation and with increasing redshift. The evolution of clusters from highly aligned and elongated systems at early times to lower alignment and elongation at present reflects the hierarchical and filamentary nature of structure formation. These measures of cluster ellipticity and alignment will provide a new test of the current cosmological model when compared with upcoming cluster surveys.Comment: 29 pages including 13 figures, to appear in ApJ Jan. 2005 (corrected typos, added reference