We consider capillary surfaces that are constructed by bounded generating curves. This class of surfaces includes radially symmetric and lower dimensional fluid-fluid interfaces. 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 pseudo-spectral method for approximating solutions to the associated boundary value problems based on interpolation by Chebyshev polynomials. This method is observably more stable than the traditional shooting method and it is computationally lean and fast. The algorithm is also adaptive, but does not use the adaptive automation in Chebfun.
翻译:我们考虑的是由捆绑的生成曲线构造的毛细表面。 这种表层包括对称和低维流体-流体-流体-流体界面。 我们使用这些表面的弧长方程表达法, 以允许生成曲线的垂直点和穿孔点。 这些考虑也包含毛细管、 悬浮滴、 废气管中的液体以及其他例子。 我们提出了一个假光谱方法, 用于根据Chebyshev 聚氨基体的内推法, 解决相关的边界值问题。 这个方法比传统的射击法更稳定, 并且具有计算精度和速度。 算法也具有适应性, 但不会在Chebfun 中使用适应性自动化。