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No full textPoznańThe paper is dealt with two kinds of multistep intervals methods which can be used to solve the initial value problem in the form of intervals containing all possible numerical errors. The interval methods of Nyström type are explicit, while the methods of Milne-Simpson are implicit. It appears that we can get two families of interval methods of the second kind. For both kinds of interval methods numerical examples are presented and compared with other interval multistep method considered in previous papers of the author
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No full textPoznańThe method of parallelization of processing in simulations of the Monte Carlo type is proposed and tested on the 3D Ashkin-Teller model characterized by a rich phase diagram. The message passing is applied and the MPI library is exploited. It is demonstrated that the method works well in different regions of the phase diagram, where the phase transitions are first-order and continuous. The dependence of speedup and efficiency on the number of parallel processes is studied. The condition for the best speedup and efficiency in these simulations is formulated and discussed using the results obtained on symmetric NUMA multiprocessor and on symmetric multicomputer. The suggestion as to effective use of the method even in highly heterogeneous computer systems is also given
