Lie group applications to the solution of differential equations

This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The project applied Lie group techniques to the solution of differential equations (DEs) describing physical systems important to LANL`s scientific mission. There were two main objectives: (1) to construct analytic or quasianalytic solutions for use as benchmark test problems; and (2) to develop improved numerical solution algorithms that possess the same symmetries (e.g. rotational, translational, and scaling invariance) as the DEs. Significant progress was achieved on both these objectives