Computing analytical solutions for PDEs through Lie symmetry method, and use of its generator through infinitesimals of a one-parameter Lie group that make invariant to an ODE by means of Maple in mathematical problems in engineering and sciences
by
R. Leticia Corral Bustamante
Instituto Tecnológico de Ciudad Cuauhtémoc, Av. Tecnológico S/N, Cd. Cuauhtémoc, Chihuahua, México.
Coauthors: David Sáenz-Z., Rigoberto Longoria-R., J. Martín Berlanga-R., Juan A. Hurtado-C., Beatriz E. Ochoa-R., Nancy I. Arana-D., Nancy Sevilla-A.

The use of the symmetry method generator of Maple to solve PDEs and integro-differential equations in engineering and sciences has given as a result successful computation of symmetries that it allows us to present arguments of evidence for a close link between the theories: General Relativity, Quantum Mechanics, and Classical Physics, with respect to the behavior of the material: an electron in an atom, several electrons traveling through an electric circuit, and, a gigantic mass such as a planet interacting in the space-time.

Einstein thought of space and time as being related and viewed the motion of the planets as being that of geodesic paths in a space-time continuum. The geodesic equations in the n-dimensional space correspond to PDEs obtained of some metric one which are computed by means of Lie symmetry method through infinitesimals (point and dynamical symmetry) of a one-parameter Lie group that make invariant to an ODE using algorithms and integration schemes to select the best integration strategy for solve equations.

The equation of Schrödinger or basic equation of the quantum mechanics as well as the function of density of space probability of classical physics solved by methods of symmetries, allow predicting very similar behavior to the geodesic equations of Einstein.

Date received: March 11, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawz-03.