Long vectors algorithms for solving grid equations of explicit difference schemes

We propose two variants of long vectors algorithms for solving grid equations of explicit difference schemes, allowing one to use the maximum number of CUDA cores even for a small dimension of the grid domain. The implementation of these algorithms is shown by the example of the heat conduction equation and the solution of Maxwell's equations. The comparison between the proposed algorithms implemented by means of the CUBLAS library and free software packages B-CALM and OpenCurrent is done.