Essentially nonnegative matrix exponential methods for nuclide transmutation

Highlights: • Two Markov chain methods are applied to nuclide transmutation. • Taylor series is used in both methods. • Algorithmic detail for software implementation is decsribed. • The high accuracy of the methods is demonstrated on demanding test problems. - Abstract: Two methods originally developed for discrete-time Markov chains are adopted for the solution of the first-order ordinary differential equation of nuclide transmutation. Both methods use Taylor series expansions, which facilitates software implementation. The methods are known, respectively, as the uniformization method and the aggressively truncated Taylor series method. The theory and algorithmic aspects of the two methods, as far as is relevant for software implementation, are presented. A few numerical test problems are employed to compare the two methods and to obtain an impression of their capabilities.