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A novel and efficient approach is proposed to calculate the dispersions of the guided modes of the photonic-crystal fibers (PCFs). Based on the vector boundary-element method (VBEM), the surface integral equations for the first and second derivatives of the propagation constants with respect to the wavelength are explicitly derived. Compared with the three-point finite-difference approach, which needs to solve and search three effective indexes near the interested wavelength, this approach can determine the dispersions of the PCFs by only solving one effective index at this wavelength based on the derived formulations. This novel approach saves over 60% computing time without losing the accuracy. Based on this approach, a novel four-ring PCF is designed by optimizing only three geometrical parameters to achieve the nearly zero ultra-flattened dispersion property. Compared with previously presented dispersion-flattened PCFs, the design procedure for the four-ring structure could be more efficient and easier because relatively lesser parameters need to be optimized.