A numerical code for the solution of the Kompaneets equation in cosmological context

Context: The cosmic microwave background (CMB) spectrum probes physical processes and astrophysical phenomena occurring at various epochs of the Universe evolution. Current and future CMB absolute temperature experiments are aimed to the discovery of the very small distortions such those associated to the cosmological reionization process or that could be generated by different kinds of earlier processes. The interpretation of future data calls for a continuous improvement in the theoretical modeling of CMB spectrum. Aims: In this work we describe the fundamental approach and, in particular, the update to recent NAG versions of a numerical code, KYPRIX, specifically written for the solution of the Kompaneets equation in cosmological context, first implemented in the years 1989-1991, aimed at the very accurate computation of the CMB spectral distortions under quite general assumptions. Methods: We describe the structure and the main subdivisions of the code and discuss the most relevant aspects of its technical implementation. Results: We present some of fundamental tests we carried out to verify the accuracy, reliability, and performance of the code. Conclusions: All the tests done demonstrates the reliability and versatility of the new code version and its very good accuracy and applicability to the scientific analysis of current CMB spectrum data and of much more precise measurements that will be available in the future. The recipes and tests described in this work can be also useful to implement accurate numerical codes for other scientific purposes using the same or similar numerical libraries or to verify the validity of different codes aimed at the same or similar problems.