Related papers: New renormalization procedure for perturbed ordina…
In this paper, we introduce the new optimal perturbation iteration method based on the perturbation iteration algorithms for the approximate solutions of nonlinear differential equations of many types. The proposed method is illustrated by…
Power series expansions naturally arise whenever solutions of ordinary differential equations are studied in the regime of perturbation theory. In the case of quasi-periodic solutions the issue of convergence of the series is plagued of the…
We derive quantum kinetic equations from a quantum field theory implementing a diagrammatic perturbative expansion improved by a resummation via the dynamical renormalization group. The method begins by obtaining the equation of motion of…
In this paper, we investigate in a unified way the structural properties of solutions to inverse problems. These solutions are regularized by the generic class of semi-norms defined as a decomposable norm composed with a linear operator,…
Here we introduce a new notion of renormalized solution to nonlinear parabolic problems with general measure data whose model is $$ \begin{cases} u_t-\Delta_{p} u =\mu & \text{in}\ (0,T)\times\Omega, u=u_0 & \text{on}\ \{0\} \times \Omega,…
We discuss the occurrence of oscillatory solutions which decay to 0 as $s\to+\infty$ for a class of perturbed second order ordinary differential equations. As opposed to other results in the recent literature, the perturbation is as small…
In the paper, we first propose a definition of renormalized solution of semilinear elliptic equation involving operator corresponding to a general (possibly nonlocal) symmetric regular Dirichlet form satisfying the so-called absolute…
The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our…
Using the renormalization group method, we improved the first order solution of the long-wavelength expansion of the Einstein equation. By assuming that the renormalization group transformation has the property of Lie group, we can…
These notes aim to provide a classical approach to solving some conformable differential equations based on prior knowledge of how to solve ordinary differential equations. That is, using the methods of separation of variables, homogeneous…
Definition of Feynman integrals as solutions of some well defined systems of differential equations is proposed. This definition is equivalent to usual one but needs no regularization and application of $R$-operation. It is argued that…
We investigate Hamiltonian systems with two degrees of freedom by using renormalization group method. We show that the original Hamiltonian systems and the renormalization group equations are integrable if the renormalization group…
New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a…
In this paper we develop a systematic reduction procedure for determining intermediate integrals of second order hyperbolic equations so that exact solutions of the second order PDEs under interest can be obtained by solving first order…
The self--similar renormalization group is used to obtain expressions for the spectrum of the Hamiltonian with the Yukawa potential. The critical screening parameter above which there are no bound states is also obtained by this method. The…
Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating…
Motivated by the study of systems of higher order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral…
We present a detailed discussion of a novel dynamical renormalization group scheme: the Dynamically Driven Renormalization Group (DDRG). This is a general renormalization method developed for dynamical systems with non-equilibrium critical…
Renormalization group procedure for effective particles in the front form of Hamiltonian dynamics is applied to an elementary quantum field theory for two species of particles mixed through a mass-like interaction term. The model…
We point out some limits of the perturbative renormalization group used in statistical mechanics both at and out of equilibrium. We argue that the non perturbative renormalization group formalism is a promising candidate to overcome some of…