Decay chain differential equations: Solutions through matrix analysis

Abstract This paper demonstrates how the solutions to conventional radioactive decay equations can be derived using results from matrix analysis. In particular, we draw on results for the matrix exponential function when the matrix is triangular. By applying key theorems, the paper explains how the solutions to these equations can be presented in algorithmic form and in terms of divided differences of the exponential function. Furthermore, with little additional effort, the approach yields solutions to more general variations of these equations.