Methods for solving the generalized nonlinear Schrodinger equation (GNLSE) with adaptive step-size methods including the local error method (LEM) and conservation quantity error method (CQEM) are described. Supercontinuum generation (SCG) in liquid-core photonic crystal fibers (PCF) is numerically simulated by using LEM and CQEM in the time domain and frequency domain (FD) respectively. According to the numerical simulation results, the advantages and disadvantages of different adaptive step-size methods are compared, and the influence of different adaptive step-size methods on the coherence of SC is analyzed. A supercontinuum (SC) spectrum spanning from approximately 1300-2800 nm with high-coherence properties is numerically generated in the 5 cm fiber with 50 fs and 1000 W pump pulses at 1.55 mu m. The numerical results demonstrate that the performance of the SC generated in FD is also better because the nonlinear operator is more effective in FD. In addition, the pulse evolution process based on LEM is smoother and the coherence is better due to its higher number of iterations and accuracy, so it is adapted to accurately modeling the SCG in PCF. However, the CQEM is more computationally efficient and can minimize the computational effort, so it is suitable for the fast modeling of SCG in PCF. This numerical study helps to optimize the numerical process of SCG and find a new way for the generation of highly coherent SC.