An Improved Maple Package for Computing Contact Symmetries of Differential Equations

• Main Authors: Je-Wei, Chang, 張哲瑋
• Other Authors: Po-Jen, Cheng
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/55411555617472595243

碩士 === 國立嘉義大學 === 應用數學系研究所 === 98 === In this thesis, we present an improved Maple package to automate the computation of contact symmetries of differential equations. Contact symmetries are the generalized surface mappings in a space that includes points and their tangents. In addition, the equations for tangency called the tangency (contact) conditions are preserved under the mapping [3]. This improved package is based upon the computer algebra system Maple, and its purpose is to find more infinitesimal generators of contact symmetry groups of a given DE than the original Maple package can get. We compare the effectiveness of our package with the function Infinitesimals in Maple 14 and the package GeM (v.0.31) developed by A. F. Cheviakov [2] by several examples. Finally, several examples are illustrated to demonstrate the application of contact symmetries.