## 5 Results  
The fixed as well as the adaptive step size fourth-order methods were successfully implemented and tested on the experimental results [43]. For validation of the numerical model, a comparison with the experimental data of [PERSON] et al. [21] was made. There, the experimental setup consisted of a lab-scale single-bed module using a pack of finned stainless-steel tubes and the composite sorbent SWS-1L. The geometrical specifications and the operating conditions of the numerical model were adjusted to their counterparts in the tested lab-scale chilling module with the adsorption/desorption bed. Inlet water heating and cooling temperatures were adjusted to 95 and 40 \({}^{\circ}\)C. Other settings, such as time control for isobaric and isosteric phases, that were the same as those in [PERSON] et al. [21] were also considered. The comparison between the time variations of the presented numerical methods and the experimental averaged bed temperatures is shown in Figure 4. To achieve results, the implemented Runge-Kutta fourth-order method, with the fixed time step \(dt=0.2\) s, required 132,952 steps; RK45, with (1e-5) accuracy, required 206,423 steps; and the Gear BDF method (accuracy 1e-2) required only 132 steps (for \(N=20\)). The accuracy was adapted to the method to make it possible to obtain results, which is associated with stability, stiffness, and other characteristic limitations of each of the presented numerical methods' calculating results based on the one-dimensional model of adsorber described above. Runge-Kutta fourth-order methods (fixed time step as well adaptive step) obtained results that were very similar, while the results based on the Gear BDF method were slightly different in several points from the Runge-Kutta results but even closer to experimental points. The reasons for the differences between the results of the experiment and the results of the numerical methods of the described model can be divided into three categories. First, the differences were related to the simplifying assumptions adopted in the model (described in point 2) regarding the constancy of some parameters, such as density, thermal conductivity, or specific heat, at variable temperatures and pressures. A simplified description of the adsorption and desorption pressures and temperatures was also assumed. The assumption of rapidly switching between adsorption and desorption cycles (cooling water is switched to hot water) also had an impact. Another aspect was the assumption of the desorption kinetics modeled as the adsorption kinetics (Equation (4)), which was a significant simplification. Second, the experimental data for validation of the model was reconstructed based on the literature and on the description of the test stand and measurement results given by the authors of [21]. According to [PERSON] et al. [21], the typical experimental error in the various tests was about 5%. Third, the discretization methods were characterized by fourth-order truncation error of approximation. In conclusion, in order to reduce the difference, a model describing the more complex heat and mass transfer could be prepared. However, the presented difference between the results of the experiment and the numerical model was at an acceptable level. Reasonable agreement between the results is an indication of proper mathematical modeling and the accuracy of the numerical schemes. For the considered one-dimensional model of the adsorber in the adsorption heat pump, one calculation case of driving parameters was chosen to investigate limitations in use of the presented numerical methods.