Abstract
Based on modern requirements for the simulation of surrogate mathematical models, the article discusses the issues of constructing implicit difference compositions that take into account not only the current behavior of the processes being studied, but also the rate of their changes. First of all, this concerns surrogate models, the implementation of which requires a numerical solution of the Cauchy problem for ordinary differential equations or their systems. The use of such single refinements contributed to a significant acceleration of convergence in the computational block, while classical block methods required iterative refinements, the number of which was no less than the dimension of the computational block. This approach contributed to a significant reduction in modeling time with obtaining results without a significant loss of accuracy, or with comparable implementation times it was possible to obtain solutions that exceed the accuracy of classical methods by an order of magnitude (orders). To conduct a comparative analysis of the speed and accuracy of numerical calculations, test tasks with known exact solutions were selected. The implementation time and calculation errors were estimated for fixed dimensions of integration steps. One-step methods with fixed dimensions of computational blocks were used as starting methods. The integration steps were specified either arbitrarily or based on restrictions imposed on the behavior of the function. The results were assessed based on the implementation time and the magnitude of the differences between the reference and numerical solutions. To construct implicit difference compositions a software application has been developed that supports the processes of generating difference compositions with arbitrary dimensions of computational blocks.
Published Version
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