Legendre spectral collocation technique for fractional inverse heat conduction problem

2021 ◽  
Author(s):  
M. A. Abdelkawy ◽  
Mohammed M. Babatin ◽  
Abeer S. Alnahdi ◽  
T. M. Taha
Keyword(s):  
Heat Conduction ◽  
Exponential Convergence ◽  
Numerical Study ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Heat Fluxes ◽  
Inverse Heat Conduction ◽  
Spectral Collocation ◽  
Independent Variables ◽  
Collocation Technique

For fractional inverse heat conduction problem (FIHCP), this paper introduces a numerical study. For the proposed FIHCP, in addition to the unknown function of temperature, the boundary heat fluxes are also unknown. Related to the two independent variables, the proposed scheme uses a fully spectral collocation treatment. Our technique is determined to be more accurate, efficient and practicable. The obtained results confirmed the exponential convergence of the spectral scheme.

scholarly journals A Meshless Method Based on the Fundamental Solution and Radial Basis Function for Solving an Inverse Heat Conduction Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Muhammad Arghand ◽  
Majid Amirfakhrian
Keyword(s):  
Heat Conduction ◽  
Fundamental Solution ◽  
Meshless Method ◽  
Heat Conduction Problem ◽  
Regularization Parameter ◽  
Linear Equations ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Radial Basis ◽  
The Stability

We propose a new meshless method to solve a backward inverse heat conduction problem. The numerical scheme, based on the fundamental solution of the heat equation and radial basis functions (RBFs), is used to obtain a numerical solution. Since the coefficients matrix is ill-conditioned, the Tikhonov regularization (TR) method is employed to solve the resulted system of linear equations. Also, the generalized cross-validation (GCV) criterion is applied to choose a regularization parameter. A test problem demonstrates the stability, accuracy, and efficiency of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document