# Implicit finite difference approximation for time fractional heat conduction under boundary condition of second kind

## DOI:

https://doi.org/10.14419/ijamr.v4i1.3783## Published:

2015-01-29## Keywords:

Boundary condition of second kind, Caputo fractional derivative, Implicit finite difference scheme, Time fractional heat conduction, Unconditionally stable.## Abstract

The time fractional heat conduction in an infinite plate of finite thickness, when both faces are subjected to boundary conditions of second kind, has been studied. The time fractional heat conduction equation is used, when attempting to describe transport process with long memory, where the rate of heat conduction is inconsistent with the classical Brownian motion. The stability and convergence of this numerical scheme has been discussed and observed that the solution is unconditionally stable. The whole analysis is presented in dimensionless form. A numerical example of particular interest has been studied and discussed in details.

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