This paper introduces a new numerical method to calculate the group delay, chromatic dispersion and dispersion slope of weakly-guiding optical fibers with arbitrary radial refractive index profiles. It is based on the analytic differentiation of the propagation coefficient up to the third order. The simulation results are compared to experimental data, with those calculated by other approaches and exact data where possible. Due to the analytical differentiation of the matrix equation, the method is more accurate compared to other approaches, it is also much faster than numerical differentiation as allows avoiding repeated solution of the eigenvalue problem to calculate the derivatives of the propagation coefficient. The precision of the method is limited only by the approximation errors of the mode solver. The Galerkin method with Laguerre-Gauss basis functions is used to determine the propagation coefficients of weakly-guiding structures. The new method enables fiber manufacturers to rapidly design dispersion characteristics of graded index, step index, single- and multiple-clad fibers, as well as few-mode and bend insensitive fibers.
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