A triangularization algorithm which determines the Lie symmetry algebra of any system of PDEs

Publisher Website
Google Scholar
Abstract
The author presents several algorithms which have been automated in the symbolic language MACSYMA. Algorithm STANDARD FORM reduces any system of linear PDEs to a simplified triangular form which has its integrability conditions identically satisfied. Generally a system's standard form is more amenable to numerical or analytical solution techniques than the system itself. The dimension of the solution space and the consistency or inconsistency of a system are directly determinable from its standard form. Algorithm TAYLOR uses a system's standard form to compute its Taylor series solution to any prescribed finite degree. The author presents an algorithm STRUCTURE CONSTANT based on STANDARD FORM and TAYLOR which, unlike existing symbolic algorithms for determining symmetries, always computes the dimension and structure constants of the Lie symmetry algebra of any system of PDEs.