以下为句子列表：
英文: A finite difference method with accuracies of fourth order in space and second order in time is proposed for time-periodic solutions of a nonlinear parabolic boundary value problem.
中文: 摘要建立了一个用于求解非线性抛物型方程时间周期解的有限差分方法，在空间和时间方向上该方法分别具有四阶和两阶精度。
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英文: Abstract: Based on photometric stereo,a new method is proposed for fabric 3-D surface reconstruction in this paper.Combining finite difference method ,the 3-D contour data of fabric is acquired,the fabric surface shape is reconstructed and analysed.
中文: 文摘:提出了一种基于光度立体视觉方法对织物进行三维表面重建.结合有限差分法,获取织物的三维轮廓数据.重建织物的表面形状并加以分析.
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英文: Based on the fourth-order difference formula of the second derivative term, a fourth-order finite difference method is developed for solving two-points boundary value problem.
中文: 摘要从中心差分公式出发，利用二阶微分的四阶差分公式，对两点边值问题得到了一种四阶精度的差分格式。
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英文: Based on the semi-vector wave equation under cylindrical coordinate system, the mode distribution and complex propagation constant in bent waveguides were computed by a finite difference method with perfectly matched layer (PML) boundary condition.
中文: 摘要以柱坐标下的半矢量波动方程为基础，采用基于完美匹配层(PML)边界条件的有限差分方法，对弯曲波导进行模式求解，进而得到波导弯曲引起的辐射损耗。
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英文: In order to improve the reliability of numerical simulation results, a new backward analysis method for mechanical parameters of slope rocks was developed based on orthogonal design, difference method and artificial neural network.
中文: 摘要为了提高数值计算结果的可靠度，基于正交设计、差分法和人工神经网络建立了新的边坡岩体力学参数反分析方法。
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