TY - JOUR
ID - 24454
TI - On convergence and stability conditions of homotopy perturbation method for an inverse heat conduction problem
JO - Iranian Journal of Numerical Analysis and Optimization
JA - IJNAO
LA - en
SN - 2423-6977
AU - â€ŽJannati, Q.
AU - Zakeri, A.
AD - Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran.
Y1 - 2015
PY - 2015
VL - 5
IS - 2
SP - 75
EP - 93
KW - Homotopy perturbation method
KW - Diffusion equation
KW - Disceretiz- ing method
KW - Inverse Problem
DO - 10.22067/ijnao.v5i2.40594
N2 - In this paper, we investigate the application of the Homotopy Perturbation Method (HPM) for solving a one-dimensional nonlinear inverse heat conduction problem. In this problem the thermal conductivity term is a linear function with respect to unknown heat temperature in bounded interval. Furthermore, the temperature histories are unknown at the end point of the interval. This problem is ill-posed. So, using the finite difference scheme and discretizing the time interval, the partial differential equation is reduced into a System of Nonlinear Ordinary Differential Equations (SNODE's). Then, using HPM, the approximated solution of the obtained Ordinary Differential Equation (ODE) system is determined. In the sequel, the stability andconvergence conditions of the proposed method are investigated. Finally, anupper bound of the error is provided.
UR - https://ijnao.um.ac.ir/article_24454.html
L1 - https://ijnao.um.ac.ir/article_24454_e5dfae1dc5a58f0fa905f373b0663990.pdf
ER -