Efficient Spectral Method for Elliptic Equations Problems in Special Areas

This paper proposes and studies a spectral method for solving elliptic problems in fan-shaped regions with Neumann boundary conditions. In theory, we transform the region to polar coordinates of [ , ] [ , ] 11 11 − − through transformation. We develop a unique and diverse style. and to construct a set of appropriate basis functions that are suitable for columnar conditions, form the problem into a matrix system, and verify its effectiveness, improving spectral accuracy through a large number of numerical examples.