REVIEW
of  bachelor's thesis "Investigation of explicit Runge-Kutta methods for Cauchy problem soluiton based on Lagrange - Burmann expansion" by A. V. Ryzhikov

Thesis of A. V. Ryzhikov is dedicated to one of the most interesting problems of computational mathematics - to the construction and investigation of numerical methods for solving the Cauchy problem for ordinary differential equations. In last years new approaches to the construction of explicit methods of solving this problem are proposed. One of such approaches based on the use of the Lagrange - Burmann expansion is proposed by E. V. Vorozhtsov. 
During his scientific work A. V. Ryzhikov dealt with the investigation of properties of explicit methods, based on the Lagrange - Burman expansion with a small number of stages. In thesis it is demonstrated, that by proper choice of method parameter and function for expansion the areas of stability domains may be indefinitely increased. These results are confirmed by the solution of stiff Cauchy problem for linear equations. Unfortunately, the problem of the parameter choice for good accuracy of the method became unresolved.
From my point of view, qualification of bachelor of Applied Mathematics and Physics is demonstrated by A. V. Ryzhikov. Thesis may be evaluated as an "excellent".

Scientific advisor,                                                candidate of science, assistant professor of the Faculty of Applied Mathematics and Processes of Control G. V. Krivovichev