Abstract
<jats:p>The article considers hybrid CPU-GPU parallel implementations of numerical solution algorithms for the hereditary model equation of radon volume activity. The test example is a direct Cauchy problem for a nonlinear fractional differential equation with a Gerasimov-Caputo operator of variable order and variable coefficients. The importance of developing efficient algorithms for solving direct problems of the radon volume activity model is due to their use in solving corresponding inverse problems based on radon monitoring data in order to solve practical problems of identifying certain parameters of the geological environment. Based on data on the average execution time of the test problem, asymptotic estimates of the complexity of sequential and proposed parallel algorithms are given. It is shown that the use of hybrid parallel CPU-GPU algorithms provides a performance gain of up to 17 times and can give a significant advantage in solving problems with large amounts of experimental data, due to the use of a GPU node. It is also shown that asymptotically exact complexity estimates are: for memory, for all hybrid algorithms of order Θ(????2); for the hybrid implementation of a non-local explicit scheme of order Θ(????); for the hybrid implementation of a non-local implicit scheme of order Θ(????2).</jats:p>