Effective methods of multisequencing of caushi problem's numeral decision for ordinary differential equations

L. P. Feldman ; O. A. Dmitrieva

Matematičeskoe modelirovanie, Tome 13 (2001) no. 7, pp. 66-72.

Résumé

The approach which is offered allowing to generate the block decision methods of ordinary differential equations on parallel calculating systems with fixed degree of accuracy. Generalization on systems of equations performs without difficulties. The convergence proofs and error estimations of onestep and multistep of block methods are described. In considered methods decision of differential equation is found in all of block points together, herewith onestep methods use only a last point of preceding block for computations in following, one whereas multistep methods use all of points of preceding block. The coefficients of difference equations for blocks with any amount of points determine by the packet Mathematical$\circledR$. Algorithms of parallel decision of nonlinear difference task are described. Estimations, describing a parallelism degree of produce methods: acceleration coefficients and effectiveness are got.