The method to get linear Caushy problem solution using parallel calculation

The method of solution the linear Cauchy problem for large systems of ordinary differential equations using parallel calculations is presented. The algorithm for linear systems of first order equations was realized by EDELWEISS computer code. This algorithm was developed especially for supercomputers that may use MPI technology to data exchange for parallel processes. The solution is presented as a row by orthogonal polynomials at $[0,1]$ segment. Features of this algorithm are simplicity, opportunity to get solution by parallel calculations and also possibility to get a solution for non-linear tasks by changing the operator using the solution from iteration process. The test problems are presented for time-dependent heat transport equation solution. Results obtained by EDELWEISS, RELAP5/MOD3.3, ANSYS and LUCKY_HEATER codes are compared.