A Useful Recurrence Formula for the Equations of Radioactive Decay

Systems of linear differential equations of the type occurring in the theory of radioactive transformations are normally solved by direct integration. For certain complex systems solutions may contain a formidable number of terms and therefore would be extremely laborious to derive. This paper presents a more practical method for solving such systems of equations. By means of a recurrence formula the method provides simple, compact, readily derivable expressions, and considerably reduces the length of numerical computation. The method is well suited for use with digital computers.