Mechanized Algorithm And Program Implementation Of One Optimal System

Symmetry group theory has an important influence in solving nonlinear equations.With the continuous development of science and technology,symbolic computation plays a more and more important role in this study as a substitution for manual computation.Based on symbolic computation and Maple software,Our thesis implements the mechanized study of one-dimensional optimal system of Lie algebra,Our main jobs are as follows:Chapter 1 introduces the relevant background and current state of nonlinear science,mathematics mechanization,symbolic computation,symmetry group theory and optimal system,then we clarify the main work of the thesis.Chapter 2 introduces some basic conceptions of the optimal system.After the clarification of Olver's method and the direct one optimal system's method,we give the mechanized algorithm flow of the new software package named OneOptimal System.And we also give the software implementation processes of KdV equation and Heat equation to clarify.Compared with existing software packages,our new mechanized algorithm has clear classification for every situation in one-dimensional optimal system.It can guarantee integrity of the system.The algorithm is more direct and programmed,then it has more possibility to expand to high-dimensional optimal system of the nonlinear equations.Chapter 3 introduces some important steps of the new software package named OneOptimalSystem with clarification of functions and parameters.And we also explain some difficult parts of implementation.Then we apply the software package to some important nonlinear equations to certificate its correctness.We can obtain the results which are the same or equal to the manual com-putation.Chapter 4 makes summary of the thesis and looks forward to the future work.