Parallel time step control of lines method for the evolution equations

Abstract

The problems of obtaining solutions for partial differential equations with the help of the method of lines are considered, which is a semi-discrete method with discretization over spatial variables. Such an approach made it possible to effectively implement a large class of evolutionary equations. The problems of solving the received SODEs by collocation block methods are considered, allowing to provide an effective parallel implementation. Moreover, all the advantages of the solution (parallel step control, local error control, stability of the solution) are realized for the case of partial derivatives without significant increase in computational complexity.