Massive parallel implementation of ODE solvers

The paper maps the possibilities of exploitation of the massive parallel computational hardware (namely GPU) for solution of the initial value problems of ordinary differential equations. Two cases are discussed: parallel solution of a single ODE and parallel execution of scalar ODE solvers. Whereas the advantages of the special architecture in the case of a single ODE are problematic, repeated solution of a single ODE for different data can prot from the parallel architecture. However, special algorithms have to be used even in the latter case to avoid code divergence be- tween individual computational threads. The topic is illustrated on several examples