We investigated a numerical scheme for the fourth-order time fractional partial differential equations by employing the temporal L2 scheme and spatial Legendre-Galerkin spectral method. The stability and error estimation of the present scheme were proved by combining partial integration, the properties of the inverse Laplace operator with respect to initial values, and the right-hand function. The error estimation indicated that the present scheme has spectral accuracy convergence in space and (3 - kappa), kappa is an element of (0, 1), uniform accuracy in time. Three numerical examples verified the theoretical convergence order in time and space.
负折射率材料是一种介电常数和磁导率同时为负的新型人工材料.到目前为止,还没有发现天然负折射率材料,所有人工负折射率材料都具有小于电磁波目标波长,但大于原子或分子组成尺寸的周期性微观结构.因此,有理由怀疑负折射率违反了物理定律.作者根据双向标量的定义,把光程标记为双向标量,然后用费马原理证明了光程为双向标量的折射定律,结果表明负折射率材料不可能存在.
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