Nonlocal Diffusion Problems That Approximate the Heat Equation with Dirichlet Boundary Conditions
نویسندگان
چکیده
We present a model for nonlocal diffusion with Dirichlet boundary conditions in a bounded smooth domain. We prove that solutions of properly re-scaled non local problems approximate uniformly the solution of the corresponding Dirichlet problem for the classical heat equation.
منابع مشابه
How to Approximate the Heat Equation with Neumann Boundary Conditions by Nonlocal Diffusion Problems
We present a model for nonlocal diffusion with Neumann boundary conditions in a bounded smooth domain prescribing the flux through the boundary. We study the limit of this family of nonlocal diffusion operators when a rescaling parameter related to the kernel of the nonlocal operator goes to zero. We prove that the solutions of this family of problems converge to a solution of the heat equation...
متن کاملAn efficient approximate method for solution of the heat equation using Laguerre-Gaussians radial functions
In the present paper, a numerical method is considered for solving one-dimensional heat equation subject to both Neumann and Dirichlet initial boundary conditions. This method is a combination of collocation method and radial basis functions (RBFs). The operational matrix of derivative for Laguerre-Gaussians (LG) radial basis functions is used to reduce the problem to a set of algebraic equatio...
متن کاملA Consistent and Accurate Numerical Method for Approximate Numerical Solution of Two Point Boundary Value Problems
In this article we have proposed an accurate finite difference method for approximate numerical solution of second order boundary value problem with Dirichlet boundary conditions. There are numerous numerical methods for solving these boundary value problems. Some these methods are more efficient and accurate than others with some advantages and disadvantages. The results in experiment on model...
متن کاملThe Existence and Behavior of Solutions for Nonlocal Boundary Problems
The existence of solutions for quasilinear parabolic equation with boundary conditions and initial conditions can be discussed by maximal regularity, and more and more works on this field show that the maximal regularity method is efficient. Here we will use some of recently results developed by H. Amann to investigate a specific boundary value problems and then apply the existence theorem to t...
متن کاملDirichlet series and approximate analytical solutions of MHD flow over a linearly stretching sheet
The paper presents the semi-numerical solution for the magnetohydrodynamic (MHD) viscous flow due to a stretching sheet caused by boundary layer of an incompressible viscous flow. The governing partial differential equations of momentum equations are reduced into a nonlinear ordinary differential equation (NODE) by using a classical similarity transformation along with appropriate boundary cond...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007