РАЗРАБОТКА И ОБОСНОВАНИЕ ПАРАЛЛЕЛЬНЫХ БЛОЧНЫХ МЕТОДОВ РЕШЕНИЯ ОБЫКНОВЕННЫХ ДИФФЕРЕНЦИАЛЬНЫХ УРАВНЕНИЙ HA SIMD-СТРУКТУРАХ

Abstract

In represented article is offered approach, allowing to generate the block decision methods of usual differential equations on parallel calculable systems with set exactness degree. Generalization on systems of equations is performed without difficulties. The convergence proofs and error estimations of onesteps and multysteps of block methods are got. In considered methods decision of differential equation is got in all of block points, herewith in first method only a last block point uses in following, whereas in second method use all of points of precedent block. The Coefficients of difference equations for blocks with any amount of points determine by the medium of packet Mathematica®. The decision on 2- and 4-pointwisse blocks are modelled. The estimations are got, describing a parallelism degree of generate methods: acceleration coefficients and effectiveness.