A new mathematical computer model for the operation of photovoltaic cells and solar hydrogen panels will be presented. It is possible to calculate the average output and efficiency as a function of certain key parameters and furthermore, calculate the optimal parameter values that achieve maximum output and maximum efficiency. Certain new external conditions can be used to significantly increase the output and efficiency to significantly larger values. This can make solar energy and hydrogen significantly cheaper, requiring smaller areas of photovoltaic cells and solar hydrogen panels and smaller initial capital investment, to achieve the required output.

The new mathematical model allows us to take into account very accurately a different rate of change in different stages of operation with the aid of dynamic equations on time scales and the Hilger derivative. An iterative computational method of successive approximations is then used to calculate numerically, to any desired accuracy, the operation of the photovoltaic cell or solar hydrogen panel, depending on the values of the key parameters and certain external conditions. Moreover, the optimal parameter values and optimal external conditions can be calculated in this model.