Related papers: Equivalence for Differential Equations
We study the rate of convergence for (variational) eigenvalues of several non-linear problems involving oscillating weights and subject to different kinds of boundary conditions in bounded domains.
Enhancing and essentially generalizing previous results on a class of (1+1)-dimensional nonlinear wave and elliptic equations, we apply several new techniques to classify admissible point transformations within this class up to the…
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…
In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial…
Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation.
We present various results on the equivalence and mapping properties under affine transformations of fractional-order Sobolev norms and semi-norms of orders between zero and one. Main results are mutual estimates of the three semi-norms of…
This paper is a new contribution to the study of regular subgroups of the affine group $AGL_n(F)$, for any field $F$. In particular we associate to any partition $\lambda\neq (1^{n+1})$ of $n+1$ abelian regular subgroups in such a way that…
Preliminary group classification for a class of generalized inviscid Burger's equations in the general form $u_t+g(x, u)u_x = f(x, u)$ is given and additional equivalence transformations are found. Adduced results complete and essentially…
We carry out the enhanced group classification of a class of (1+1)-dimensional nonlinear diffusion-reaction equations with gradient-dependent diffusivity using the two-step version of the method of furcate splitting. For simultaneously…
We give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of the third order on a two dimensional manifold and show their application to the equivalence problem of such…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
The role of differential equations in the process of calculating Feynman integrals is reviewed. An example of a diagram is given for which the method of differential equations was introduced, the properties of the inverse-mass-expansion…
The Cauchy problem for fractional derivatives linear systems of ordinary differential equations with constant coefficients is considered, where at first the analytic expressions are given through the matrix exponent of its corresponding…
A systematic and unified approach to transformations and symmetries of general second order linear parabolic partial differential equations is presented. Equivalence group is used to derive the Appell type transformations, specifically…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
The article concerns the problem if a~given system of differential equations is identical with the Euler--Lagrange system of an~appropriate variational integral. Elementary approach is applied. The main results involve the determination of…
We compute invariants for the two-variable M\"obius transformation. In particular we are interested in partial differential equations in two dependent and two independent variables that are kept invariant under this transformation.
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…
Quantum affine bundles are quantum principal bundles with affine quantum structure groups. A general theory of quantum affine bundles is presented. In particular, a detailed analysis of differential calculi over these bundles is performed,…