We consider radially symmetric capillary surfaces that are described by bounded generating curves. We use the arc-length representation of the differential equations for these surfaces to allow for vertical points and inflection points along the generating curve. These considerations admit capillary tubes, sessile drops, and fluids in annular tubes as well as other examples. We present a multi-scale pseudo-spectral method for approximating solutions of the associated boundary value problems based on interpolation by Chebyshev polynomials. The multi-scale approach is based on a domain decomposition with adaptive refinements within each sub-domain.

翻译：本文考虑由有界生成曲线描述的径向对称毛细表面。采用弧长表示法描述这些表面的微分方程，从而允许生成曲线上存在垂直点和拐点。这些分析涵盖了毛细管、座滴、环形管中的流体及其他实例。我们提出了一种基于切比雪夫多项式插值的多尺度伪谱方法，用于近似求解相关的边值问题。该多尺度方法基于区域分解，并在每个子区域内进行自适应加密。