We report the formulation of the adaptive variable coefficient predictor-corrector Adams-Bashforth scheme for modeling the population dynamics in erbium-doped fiber amplifiers and lasers based on highly doped fibers. A modified form of the scheme derived using a Lagrange polynomial is shown to result in 75% reduction of step-size as compared to a conventional adaptive Euler method. Our analysis shows that the second-order predictor and third-order corrector is most suitable for accurate modeling of the above problem. The model has been validated by re-generating the absorption and emission spectrum for doped fibers found in the literature. This modeling approach has been carried further to simulate a filterless fiber laser cavity, in which several gain and saturation dynamics are encountered. Spectral power evolution in the fiber is simulated by using the above method, and the steady-state lasing wavelength is evaluated as a function of cavity attenuation. The experimental results are found to match very well with the simulation.