Comparative evaluation of cubic spline, Akima, and PCHIP interpolation methods for predicting radiation shielding parameters of heavy metal oxide glasses

Mathematical modeling was carried out to better examine the shielding behavior of glasses with the composition 65B 2 O 3 –25PbO–10M, where M represents Sb 2 O 3 , Al 2 O 3 , or ZnO. Since the tabulated values are available only at specific energies, additional points were estimated using three interpolation schemes: Cubic Spline, PCHIP, and Akima. The analysis focused on LAC, TVL, and Z eff in order to see how each method responds to changes in energy and shielding parameter. As an example, the XCOM TVL for the Al glass at 0.3443 MeV is equal to 2.6882 cm, while the Akima value is 2.6880 cm, while at 0.9641 MeV they are respectively equal to 7.7200 and 7.7250 cm. The models were also compared against each other to understand the pros and cons of each method, finding that depending on the energy range and the parameter analyzed, each of the three methods has its advantages. This work stands out for its balanced comparison of Cubic Spline, PCHIP, and Akima interpolation within the same 65B 2 O 3 –25PbO–10M glass system. It evaluates them under identical conditions and links the numerical differences directly to shielding parameters, providing a practical basis for selecting the most suitable modeling approach.