Mathematical modeling of species transformations in aquatic sediments is usually based on numerical solutions to the same general one-dimensional mass-conservation equation and is likely to require substantial computation time. In this paper we present a fast numerical solution to this equation. The solution is suited for both single and multi-component models and it is based on an implicit control volume discretization of the general mass-conservation equation. The solution consists of two algorithms, one that decomposes the discretization matrix once and one that subsequently produces multiple solutions with minimal computational effort. A unique feature of these algorithms is that values of boundary conditions can vary as a simulation progresses without requiring new decompositions of the discretization matrix. This feature can reduce computation time significantly relative to commonly used procedures for modeling dynamic systems. Finally, we present four examples in which the numerical solution is applied to specific problems. From these examples guidelines are derived for the discretization in space and time required to obtain precise solutions of the general mass-conservation equation.