Abstract
In this work we study the numerical solution of one-dimensional heatdiffusion equation with a small positive parameter subject to Robin boundary conditions. The simulations examples lead us to conclude that the numerical solutionsof the differential equation with Robin boundary condition are very close of theanalytic solution of the problem with homogeneous Dirichlet boundary conditionswhen tends to zero
Highlights
It is well known that the diffusion differential equation models the transient conduction phenomenon that occurs in numerous engineering applications and may be analyzed by using different analytic and numerical methods
If ε = 0 in (1.1) we have the classical problem with homogeneous Dirichlet boundary conditions for the heat equation which is well known
Our little contribution with this kind of problems which depend of a small parameter is to show numerical solutions when we vary the values of ε
Summary
It is well known that the diffusion differential equation models the transient conduction phenomenon that occurs in numerous engineering applications and may be analyzed by using different analytic and numerical methods. Many transient problems involving geometry and simple boundary value conditions, their analytic solution are known explicitly, especially the onedimensional (1D) case. In most cases, the geometry or boundary conditions make it impossible to apply analytic techniques to solve the heat diffusion equation. The particular (1.1) problem with singular boundary conditions, depending on a positive parameter, has not been studied previously neither analytically nor numerically. Many problems in the industry are modeled by the heat equation subject to specific initial and boundary conditions, and sometimes it is not possible to get the analytic solution.
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