The modeling of batch crystallization involves a population balance to get the crystal size distribution which is one of the most important properties in this process. Thus, this model leads to a system of integral, partial differential and algebraic equations (IPDAE). This system can be easily solved by finite difference methods with uniform discretization. However to increase the calculation efficiency and the crystal size distribution accuracy, an adaptive finite difference method with a non-uniform discretization was developed. Results of both methods are compared in term of efficiency and are confronted to experimental data in term of accuracy.