کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
401403 | 675351 | 2009 | 16 صفحه PDF | دانلود رایگان |

The goal of the present paper is to propose an enhanced ordinary differential equation solver by exploitation of the powerful equivalence method of Élie Cartan. This solver returns a target equation equivalent to the equation to be solved and the transformation realizing the equivalence. The target ODE is a member of a dictionary of ODEs, that are regarded as well-known, or at least well-studied. The dictionary considered in this article comprises the ODEs in a book of Kamke. The major advantage of our solver is that the equivalence transformation is obtained without integrating differential equations. We provide also a theoretical contribution revealing the relationship between the change of coordinates that maps two differential equations and their symmetry pseudo-groups.
Journal: Journal of Symbolic Computation - Volume 44, Issue 7, July 2009, Pages 836-851