A Java framework for massively distributed symbolic computing
Laurent Bernardin · ACM SIGSAM Bulletin · 1999
Different analytical methods available for the solution of radioactive decay chains have been implemented in Mathematica.The implemented algorithms include the method of dagonalization, the Laplace transformation, Matrix Exponential Method, Bateman solution and the E formulation.These methods have been programmed in Mathematica by defining the functions for each method separately.These functions require only the decay constants.There is no limitation on the number of members of decay chains.Each algorithm has been tested for different sets of decay constants.These methods differ only in execution time.Laplace transformation is the slowest method while Bateman and E formulation proves to be the fastest ones.Method of diagonalization and forward sequential method, both use built-in function DSovle, take comparable time for execution.Matrix Exponential Method is also less time consuming in comparision to Forward sequential and Method of diagonalization, however it fails in the case of singularities.This failure may be prevented by avoiding the singularity.The methods may be extended to the chains where branching also occurs.Computing the Galois Group of y(3) + ay' + by = 0, a, b E C [x]