Prof. Mir Sajjad Hashemi
Prof. Mir Sajjad Hashemi
University of Bonab, Iran
Title: Applications of Lie groups to the differential equations-Analytical and numerical approaches
One of the important roles in the study of nonlinear physical systems described with a differential equation, is the investigation of their solutions. A systematic and powerful method to derive the exact solutions of nonlinear differential equations is Lie symmetry method which some important properties such as conservation laws, can successfully be obtained using the symmetries. Lie groups have also advantages in extracting the numerical approaches. Among the many existing numerical algorithms, the Group Preserving Scheme (GPS) is a numerical method based upon Lie group solvers that preserves the Lie group structure under discretization. This method uses the Cayley transformation and the Pad´e approximations in the augmented Minkowski space Mn+1. One of the major benefits of GPS in the Mn+1 is that it can avoid ghost fixed points and spurious solutions.
Professor Mir Sajjad Hashemi holds a PhD. in applied mathematics from Imam Khomeini International University (Iran) and M.A. degree from the Tabriz University (Iran). He is vice-chancellor in University of Bonab from 2013 until now. He is supervisor of two PhD. and 13 M.A. degree defensed students. His primary research interests are in the field of Lie theory and its applications to the differential equations (Ordinary, partial, fractional). Analytical and approximate solutions of ODEs, PDEs and fractional PDEs with various methods specifically with geometric methods are his other main research fields.