Meshcheryakov Laboratory of Information Technologies

Date and Time: Thursday, 3 June 2021, at 3:00 PM

Venue: Online seminar on Webex, Laboratory of Information Technologies

More information about the seminar and the link to connect via Webex

Seminar topic: “Numerical Solution of the Cauchy Problem Based on The Basic Element Method”

Speaker: N. D. Dikusar

Abstract:

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.