REVIEW
of  bachelor's thesis "Investigation of Runge-Kutta methods with high order of accuracy" by M. S. Panchenko

Thesis of M. S. Panchenko 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. It should be noted, that this problem may be considered not only as an independent mathematical model, but also as a result of the application of semi-disretization method  to initial boundary value problems of mathematical physics. In this case, stability problem is considered as one of the main problems. Due to the high order of the obtained systems, problem of the application of explicit method with high accuracy order with small number of stages is considered.
 The approach to improving of the stability of high order methods proposed in the early 2000s by D. Goeken and O. Johnson is realized in presented thesis. The basic idea involves the finding the values ​​of  method parameters, which maximize the areas of stability domains. In thesis this method is implemented to the case of methods of three stages. During solution of test problems for equations of mathematical physics it is demonstrated, that usage of optimal parameters actually may improve the stability of explicit numerical methods.
From my point of view, qualification of bachelor of Applied Mathematics and Physics is demonstrated by M. S. Panchenko. 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