A characterization of caloric morphisms between manifolds.
A Computer Algebra Application to Determination of Lie Symmetries of Partial Differential Equations
The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006A MATHEMATICA package for finding Lie symmetries of partial differential equations is presented. The package is designed to create and solve the associated determining system of equations, the full set of solutions of which generates the widest permissible local Lie group of point symmetry transformations. Examples illustrating the functionality of the package's tools...
A conservative finite difference scheme for static diffusion equation.
A control on the set where a Green's function vanishes
A Direct Approach to the Mellin Transform.
A Discrete Sampling Inversion Scheme for the Heat Equation.
A domain splitting method for heat conduction problems in composite materials
A domain splitting method for heat conduction problems in composite materials
We consider a domain decomposition method for some unsteady heat conduction problem in composite structures. This linear model problem is obtained by homogenization of thin layers of fibres embedded into some standard material. For ease of presentation we consider the case of two space dimensions only. The set of finite element equations obtained by the backward Euler scheme is parallelized in a problem-oriented fashion by some noniterative overlapping domain splitting method, eventually enhanced...
A final value problem for heat equation: regularization by truncation method and new error estimates.
A generalized Nevanlinna theorem for supertemperatures.
A gradient estimate for solutions of the heat equation
A gradient estimate for solutions of the heat equation. II
The author obtains an estimate for the spatial gradient of solutions of the heat equation, subject to a homogeneous Neumann boundary condition, in terms of the gradient of the initial data. The proof is accomplished via the maximum principle; the main assumption is that the sufficiently smooth boundary be convex.
A heat approximation
The Fourier problem on planar domains with time variable boundary is considered using integral equations. A simple numerical method for the integral equation is described and the convergence of the method is proved. It is shown how to approximate the solution of the Fourier problem and how to estimate the error. A numerical example is given.
A heat conduction problem involving phase change and its numerical solution by finite difference methods
A Heat Semigroup Version of Bernstein's Theorem on Lie Groups.
A high-order difference scheme for a nonlocal boundary-value problem for the heat equation.
A Method for the Numerical Solution of the One-Dimensional Inverse Stefan Problem.
A minorization of the first positive eigenvalue of the scalar laplacian on a compact Riemannian manifold [Book]
A mixed boundary value problem for heat potentials (Preliminary communication)
A new error estimate for a fully finite element discretization scheme for parabolic equations using Crank-Nicolson method
Finite element methods with piecewise polynomial spaces in space for solving the nonstationary heat equation, as a model for parabolic equations are considered. The discretization in time is performed using the Crank-Nicolson method. A new a priori estimate is proved. Thanks to this new a priori estimate, a new error estimate in the discrete norm of is proved. An -error estimate is also shown. These error estimates are useful since they allow us to get second order time accurate approximations...