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Application of Generalized Finite Difference Method in Analysis of Transmission Characteristics of Waveguide

The generalized finite difference method(GFDM) is a collocation-type meshless method. It is a numerical calculation method that approximates the partial derivatives of various orders by the linear combination of function values at adjacent nodes and finally solves the differential equation. This method uses Taylor series expansion and least squares method to obtain the display formula of the partial derivative of the unknown variables, which overcomes the dependence of the traditional finite difference method on the grid. In this paper, the GFDM is applied to the analysis of the mode characteristics of waveguides, and the numerical discrete scheme of the GFDM for the eigenvalue problems is established. Numerical results show that the proposed algorithm is effective and stable, which provides a new idea for solving the dispersion characteristic of the waveguide.