We consider the Degasperis-Procesi equation, which was recently introduced as a completely integrable shallow water equation. We propose nonlinear and linear finite difference schemes for the equation based on an extended version of the discrete variational derivative method, and show that they preserve two associated invariants at a same time. We also prove the unique solvability of the schemes, and evaluate the schemes numerically.
In this paper, we propose a numerical procedure based on FDTD (Finite Difference Time Domain) method with PML (Perfectly Matched Layer) where we model an antenna as a highly conducting region in three dimensional domain. We apply the procedure to several antennas to verify its effectiveness. In the PML region, we apply a new discretization scheme proposed by the present authors in one dimensional case. The electric current in the antenna is computed afterwards from the surrounding magnetic field. The numerical results show a good performance of our method.
Nerve actions generate current distribution and evoke magnetic field outside the body. Magnetospinography (MSG) visualizes signal transfer on spinal cord by measuring and analyzing magnetic field evoked by the signal transfer. It can be used in localization of spinal cord damage. This paper treats some problems on the existing model for magnetic sources on MSG and reveals the cause of the problems. Furthermore, the author proposes a new model and shows its superiority over existing one.
A rich variety of iterative methods based on IDR (Induced Dimension Reduction) Theorem have been proposed, and their excellent convergence attracts attention. We construct an accelerated variant of IDR(s) method using the iteration matrix of the SOR (Successive Over-Relaxation) method. In this paper, we propose IDR(s)-based SOR method. A number of numerical experiments verify efficiency and robustness of convergence of the IDR(s)-based SOR method compared with several conventional iterative methods.