Derived was the scalar wave equation of optical fibers. Based on the derived equation, the dispersion characteristics of arbitrarily profiled fibers were analyzed. We applied the 1-D FEM employing quadratic interpolation fucntions to solve the scalar wave equation. To find the optimum index distribution of a fiber that has the ultra-low total dispersion, we analyzed QC fibers as objects. Adding 2$_{nd}$ and 3$_{rd}$ clads to DC fiber, we investigated the change of dispersion characteristics. We found the QC fiber parameters for which the dispersion was ultra-low flattened, less than 0.5 ps/km.nm for ${lambda}=1.4~1.6{mu}m$, and the dispersion value was as low as 0.20 ps/km.nm at ${lambda}=1.55{mu}m$