Solar cosmic rays are generated in the solar atmosphere, while their registration is carried out in interplanetary space in most events in the Earth’s orbit. To establish a relationship between the registered intensity of solar cosmic rays and the intensity at the source, it is necessary to take into account its change during injection and propagation in interplanetary space. During diffusion propagation of particles in the case of a non-stationary source, a strong change in the spatial distribution of particles occurs, which complicates the application of numerical solution methods. Here, we offer a solution method based on using a quasi-self-similar variable. The method allows obtaining a quasi-self-similar variable and a missing boundary condition, guaranteeing the conservation of the total number of diffusing particles. Comparison of the obtained numerical solution with the known exact solution for a point source impulsed in time shows sufficient accuracy except for a small vicinity of the source. We have solved the case with a non-stationary point source. The balance between the total numbers of injected and diffusing particles, depending on the time, shows sufficient accuracy for the solution. The obtained numerical solutions confirm the method’s applicability for calculating the non-stationary equation of particle transport in an infinite space.
Petukhov et al. (2025) studied this question.