Thursday, June 3, 2021 15:00 MLIT Conference Hall, Online seminar via Webex N.D. DikusarNumerical Solution of the Cauchy Problem Based on The Basic Element Method An explicit method has been developed for the numerical solution of the Cauchy initial problem for ordinary differential equations according to the `predictor-corrector` scheme based on two polynomials of the fifth degree in the form of the basic elements (BEM-polynomials). To calculate the coefficients of BEM-polynomials, the values of the function and of its first derivative at the grid nodes and two setting parameters h and K are used. The method has the fifth order of precision with double request to the right side. It is shown that the error of the method is not worse than the errors of the popular classical Runge-Kutta methods of the fourth order, Adams-Bashforth and Fehlberg of the fifth order. The stability of the method in calculations with an excessively small grid step h = 10-17, 10-15 makes it promising in relations of solving stiff problems. More information on the seminar and the link to connect via Webex are available at Indico.