Институт вычислительной математики и математической геофизики СОРАН

Abstracts

This report proposes the new constructions for splitting partial differential equations in two-dimensional and three-dimensional space. Conclusion of the new methods is based on the diagonally implicit methods of the second for fourth orders. The parameters of the methods were selected so that the methods remained absolutely and unconditionally stable.

The true representation of the diagonally implicit forms in ordinary differential equations reduce to difficult program realization for the methods in many-dimensional evolutionary equations. That is required to change the diagonally implicit forms that as the methods there are simple program realization, moreover the methods remained high order of approximation and unconditionally stable. This is a new approach to the construction the splitting diagonally implicit methods.

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