Algorithm 982: Explicit Solutions of Triangular Systems of First-Order Linear Initial-Value Ordinary Differential Equations with Constant Coefficients. A method to compute explicit solutions of homogeneous triangular systems of first-order linear initial-value ordinary differential equations with constant coefficients is described. It is suitable for the limited case of well separated eigenvalues, or for multiple zero eigenvalues provided the entire column corresponding to a zero eigenvalue is zero. The solution for the case of constant inhomogeneity is described. The method requires only the computation of a constant matrix using a simple recurrence. Computing the solutions of the system from that matrix, for values of the independent variable, requires one to exponentiate only the diagonal of a matrix. It is not necessary to compute the exponential of a general triangular matrix. Although this work was motivated by a study of nuclear decay without fission or neutron absorption, which is used throughout as an example, it has wider applicability.

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