A diffusion-limited model has been used to describe supersaturation in liquid phase epitaxy (LPE). LPE is not often treated in chemical engineering, but the equations in a diffusion-limited model are similar to those used in thermal engineering. Therefore, we can deal with these equations analytically and solve them numerically. This paper solves the problem that the numerical solutions of the diffusion-limited model depend on the mesh sizes and comprises two parts. The first part provides an update of the traditional equation to describe the initial condition in the diffusion-limited model. The second part is a proposal of methods to calculate the compositional variation using the diffusion-limited model. The mesh sizes for the numerical simulations are determined systematically to calculate the solid phase composition within a desired tolerance limit.