We are glad to bring to your attention a new preprint «A Three-Point Grid Based Polynomial Prediction» P5-2020-1 published by the JINR Publishing Department. The author of the paper is N. D. Dikusar.

Abstract:

Within the framework of the recently proposed basic element method (BEM), a new approach is made to the solution of the problem of polynomial prediction and extrapolation of the sixth order for smooth functions. The one step forward forecast is performed using two fifth degree polynomials. The formulae for the coefficients of BEM-polynomials depend on the grid step, the values of the function and its first derivative at the nodes of two three-point grids. The method was tested on the numerical solution of the Cauchy problem for ODE. The efficiency of numerical integration is ensured by a threefold calculation of the right side of the equation and the O(h⁵) accuracy of the solution. The BEM-prediction can serve as the core for the development and creation of effective algorithms for numerically solving Cauchy problems for ODEs, including stiff ones.

The investigation has been performed at the Laboratory of Information Technologies, JINR.

Read the full version (in Russian)