Maximum norm error estimates of efficient difference schemes for second-order wave equations

AbstractThe three-level explicit scheme is efficient for numerical approximation of the second-order wave equations. By employing a fourth-order accurate scheme to approximate the solution at first time level, it is shown that the discrete solution is conditionally convergent in the maximum norm with the convergence order of two. Since the asymptotic expansion of the difference solution consists of odd powers of the mesh parameters (time step and spacings), an unusual Richardson extrapolation formula is needed in promoting the second-order solution to fourth-order accuracy. Extensions of our technique to the classical ADI scheme also yield the maximum norm error estimate of the discrete solution and its extrapolation. Numerical experiments are presented to support our theoretical results

Maximum norm error estimates of the Crank–Nicolson scheme for solving a linear moving boundary problem

AbstractThe Crank–Nicolson scheme is considered for solving a linear convection–diffusion equation with moving boundaries. The original problem is transformed into an equivalent system defined on a rectangular region by a linear transformation. Using energy techniques we show that the numerical solutions of the Crank–Nicolson scheme are unconditionally stable and convergent in the maximum norm. Numerical experiments are presented to support our theoretical results

The hidden strange BcB_{c}-like molecular states

With the chiral unitary approach, we evaluate the hidden strange $B_{c}$-like molecular states of $b\bar{c}s\bar{s}$ systems $\bar{B}_{s}\bar{D}_{s}$, $\bar{B}_{s}^{*}\bar{D}_{s}$, $\bar{B}_{s}\bar{D}_{s}^{*}$, and $\bar{B}_{s}^{*}\bar{D}_{s}^{*}$ coupled to the non-strange channels. The $S$-wave scattering amplitudes are calculated based on the vector meson exchange, four pseudoscalar mesons contact interactions, and four vector mesons contact interactions obtained from the extended local hidden gauge approach. We find six states below the threshold of the most relevant channel. The binding energies of these states are around $1-10$ MeV and the widths are around $0.2-0.7$ MeV. Our research is a supplement to the mass spectra of $B_{c}$-like states, which may be useful for the experimental search in the future.Comment: 15 pages, 8 figure

tert-Butyl 2-borono-1H-pyrrole-1-carboxyl­ate

In the crystal structure of the title compound, C9H14BNO4, the boronic acid group and carbamate groups are nearly co-planar with the pyrrole ring, making dihedral angles of 0.1 (2) and 2.2 (2)°, respectively. Intra­molecular and inter­molecular O—H⋯O hydrogen bonds help to stabilize the structure, the latter interaction leading to inversion dimers.

Methyl 4-methyl­sulfonyl-2-nitro­benzoate

The title compound, C9H9NO6S, was prepared by the reaction of methanol and thionyl chloride with 4-methyl­sulfonyl-2-nitro­benzoic acid under mild conditions. The dihedral angle between the nitro group and benzene ring is 21.33 (19)° and that between the carboxyl­ate group and the benzene ring is 72.09 (17)°. The crystal structure is stabilized by weak inter­molecular bifurcated C—H⋯O inter­actions occurring in the (100) plane

Ethyl N-[3-(N,N-dimethyl­carbamo­yl)pyridin-2-ylsulfon­yl]carbamate

In the mol­ecular structure of the title compound, C11H15N3O5S, the amide group is nearly perpendicular to the pyridine ring, making a dihedral angle of 86.30 (13)°. The terminal ethyl group is disordered over two sites of equal occupancy. Inter­molecular N—H⋯O hydrogen bonding is present in the crystal structure