相关论文: The Differential Form Method for Finding Symmetrie…

Partial differential equations can be used for extracting geometric features of shapes. This article summarizes recent methods to extract the normal vector field from an elliptic equation proposed by Yamada and from the heat equation, and…

We present a subdivision method to solve systems of congruence equations. This method is inspired in a subdivision method, based on Bernstein forms, to solve systems of polynomial inequalities in several variables and arbitrary degrees. The…

A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…

This paper introduces a new difference scheme to the difference equations for N-body type problems. To find the non-collision periodic solutions and generalized periodic solutions in multi-radial symmetric constraint for the N-body type…

We give a brief introduction to Hamiltonian optics and Lie algebraic methods. We use these methods to describe the operators governing light propagation, refraction and reflection in phase space. The method offers a systematic way to find…

We consider a system of partial differential equations, of interest to plasma physics, and provide all its Lie point symmetries, with their respective invariant solutions. We also discuss some of its conditional and partial symmetries. We…

A method is introduced for the construction of meshless discretization schemes which preserve Lie symmetries of the differential equations that these schemes approximate. The method exploits the fact that equivariant moving frames provide a…

The method of characteristics has played a very important role in mathematical physics. Preciously, it was used to solve the initial value problem for partial differential equations of first order. In this paper, we propose a fractional…

A spectral decomposition method is used to obtain solutions to a class of nonlinear differential equations. We extend this approach to the analysis of the fractional form of these equations and demonstrate the method by applying it to the…

An algorithmic method to exploit a general class of infinitesimal symmetries for reducing stochastic differential equations is presented and a natural definition of reconstruction, inspired by the classical reconstruction by quadratures, is…

The different natures of approximate symmetries and their corresponding first integrals/invariants are delineated in the contexts of both Lie symmetries of ordinary differential equations and Noether symmetries of the Action Integral.…

In [7], a new iterative method for solving linear system of equations was presented which can be considered as a modification of the Gauss-Seidel method. Then in [4] a different approach, say 2D-DSPM, and more effective one was introduced.…

This primer is intended as an introduction to differential forms, a central object in modern mathematical physics, for scientists and engineers.

A discussion is presented, within a simple unifying scheme, about different types of symmetry of PDE's, with the introduction and a precise characterization of the notions of "standard" and "weak" conditional symmetries, together with their…

This paper presents a brief account of the important milestones in the historical development of the theory of differential equations. The paper begins with a discussion on the date of birth of differential equations and then touches upon…

Using Lie symmetry methods for differential equations we have investigated the symmetries of a Lagrangian for a plane symmetric static spacetime. Perturbing this Lagrangian we explore its approximate symmetries. It has a non-trivial…

A geometrical formulation for adjoint-symmetries as 1-forms is studied for general partial differential equations (PDEs), which provides a dual counterpart of the geometrical meaning of symmetries as tangent vector fields on the solution…

This paper presents a new Lie theoretic approach to fractal calculus, which in turn yields such new results as a Fractal Noether's Theorem, a setting for fractal differential forms, for vector fields, and Lie derivatives, as well as…

We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…

Stochastic differential equations (sdes) play an important role in physics but existing numerical methods for solving such equations are of low accuracy and poor stability. A general strategy for developing accurate and efficient schemes…