ﻻ يوجد ملخص باللغة العربية
We derive the discretized Maxwells equations using the discrete variational derivative method (DVDM), calculate the evolution equation of the constraint, and confirm that the equation is satisfied at the discrete level. Numerical simulations showed that the results obtained by the DVDM are superior to those obtained by the Crank-Nicolson scheme. In addition, we study the two types of the discretized Maxwells equations by the DVDM and conclude that if the evolution equation of the constraint is not conserved at the discrete level, then the numerical results are also unstable.
We propose a new numerical scheme of evolution for the Einstein equations using the discrete variational derivative method (DVDM). We derive the discrete evolution equation of the constraint using this scheme and show the constraint preserves in the
We present a previously unexplored forward-mode differentiation method for Maxwells equations, with applications in the field of sensitivity analysis. This approach yields exact gradients and is similar to the popular adjoint variable method, but pro
We present a positive and asymptotic preserving numerical scheme for solving linear kinetic, transport equations that relax to a diffusive equation in the limit of infinite scattering. The proposed scheme is developed using a standard spectral angula
We study the essential spectrum of operator pencils associated with anisotropic Maxwell equations, with permittivity $varepsilon$, permeability $mu$ and conductivity $sigma$, on finitely connected unbounded domains. The main result is that the essent
Theories of gravity other than general relativity (GR) can explain the observed cosmic acceleration without a cosmological constant. One such class of theories of gravity is f(R). Metric f(R) theories have been proven to be equivalent to Brans-Dicke