Related papers: Approximate Q-conditional symmetries of partial di…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
We advance an exact, explicit form for the solutions to the fractional diffusion-advection equation. Numerical analysis of this equation shows that its solutions resemble power-laws.
The paper investigates solutions of the fractional hyperbolic diffusion equation in its most general form with two fractional derivatives of distinct orders. The solutions are given as spatial-temporal homogeneous and isotropic random…
Approximate group analysis technique, that is, the technique combining the methodology of group analysis and theory of small perturbations, is applied to finite-difference equations approximating ordinary differential equations.…
Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can…
We study conservation laws and potential symmetries of (systems of) differential equations applying equivalence relations generated by point transformations between the equations. A Fokker-Planck equation and the Burgers equation are…
We develop a quasi-chemical theory for the study of packing thermodynamics in dense liquids. The situation of hard-core interactions is addressed by considering the binding of solvent molecules to a precisely defined `cavity' in order to…
Some transformations acting on radially symmetric solutions to the following class of non-homogeneous reaction-diffusion equations $$ |x|^{\sigma_1}\partial_tu=\Delta u^m+|x|^{\sigma_2}u^p, \qquad (x,t)\in\real^N\times(0,\infty), $$ which…
Time fractional advection-dispersion equations arise as generalizations of classical integer order advection-dispersion equations and are increasingly used to model fluid flow problems through porous media. In this paper we develop an…
Variational methods based on optimization strategies are proposed to numerically solve a large family of nonlinear partial differential equations. They are all particular instances of gradient flows with general costs, including the…
In this paper, we consider a q-analogue of the Borel-Laplace summation where q>1 is a real parameter. In particular, we show that the Borel-Laplace summation of a divergent power series solution of a linear differential equation can be…
In this paper, we prove a result of equivalence in law between a diffusion conditioned with respect to partial observations and an auxiliary process. By partial observations we mean coordinates (or linear transformation) of the process at a…
In this paper, approximate optimality conditions and sensitivity analysis in nearly convex optimization are discussed. More precisely, as in the spirit of convex analysis, we introduce the concept of $\varepsilon$-subdifferential for nearly…
A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They take solutions into solutions and can be…
For a generalized Hodge Laplace equation, we prove the quasi-optimal convergence rate of an adaptive mixed finite element method. This adaptive method can control the error in the natural mixed variational norm when the space of harmonic…
We derive a method for finding Lie Symmetries for third-order difference equations. We use these symmetries to reduce the order of the difference equations and hence obtain the solutions of some third-order difference equations. We also…
In this paper, the classical and quantum solutions of some axisymmetric cosmologies coupled to a massless scalar field are studied in the context of minisuperspace approximation. In these models, the singular nature of the Lagrangians…
A generalisation of the Lie symmetry method is applied to classify a coupled system of reaction-diffusion equations wherein the nonlinearities involve arbitrary functions in the limit case in which one equation of the pair is quasi-steady…
We prove nonlinear lower bounds and commutator estimates for the Dirichlet fractional Laplacian in bounded domains. The applications include bounds for linear drift-diffusion equations with nonlocal dissipation and global existence of weak…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…