The Renormalization Group as a Method for Analyzing Differential Equations
نویسنده
چکیده
By following hints derived from similarities between critical phenomena and the theory of qualitatively significant (i.e. singular) perturbations to ordinary differential equations, a renormalization group method of analyzing singular perturbations in differential equations is developed. This method is applied to the Raleigh Equation to develop the method explicitly. Other recent work is briefly discussed, and prospects for future work.
منابع مشابه
Time-Dependent Real-Space Renormalization Group Method
In this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent Hamiltonians. We drive the time-dependent recursion relations for the renormalized tight-binding Hamiltonian by decimating selective sites of lattice iteratively. The formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...
متن کاملA Geometrical Formulation of the Renormalization Group Method for Global Analysis II: Partial Differential Equations
It is shown that the renormalization group (RG) method for global analysis can be formulated in the context of the classical theory of envelopes: Several examples from partial differential equations are analyzed. The amplitude equations which are usually derived by the reductive perturbation theory are shown to be naturally derived as the equations describing the envelopes of the local solution...
متن کاملCascade of Fractional Differential Equations and Generalized Mittag-Leffler Stability
This paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional different...
متن کاملLie-Group Approach to Perturbative Renormalization-Group Method
The Lie-group approach to the perturbative renormalization group (RG) method is developed to obtain an asymptotic solutions of both autonomous and non-autonomous ordinary differential equations. Reduction of some partial differetial equations to typical RG equations is also achieved by this approach and a simple recipe for providing RG equations is presented.
متن کاملReduction of Differential Equations by Lie Algebra of Symmetries
The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...
متن کامل