Stabilizing the nonlinear spherically symmetric backward heat equation via two-parameter regularization method

2017 ◽  
Vol 19 (4) ◽  
pp. 2461-2481 ◽  
Author(s):  
Tra Quoc Khanh ◽  
Tran Thi Khieu ◽  
Ngo Van Hoa
Keyword(s):  
Heat Equation ◽  
Regularization Method ◽  
Spherically Symmetric ◽  
Parameter Regularization ◽  
Two Parameter

scholarly journals Two-Parameter Regularization Method for a Nonlinear Backward Heat Problem with a Conformable Derivative

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Vu Ho ◽  
Donal O’Regan ◽  
Hoa Ngo Van
Keyword(s):  
Integral Equation ◽  
Regularization Method ◽  
Time Variable ◽  
Conformable Derivative ◽  
Heat Problem ◽  
Regularization Parameters ◽  
Ill Posed ◽  
Parameter Regularization ◽  
Two Parameter ◽  
Backward Heat Problem

In this paper, we consider the nonlinear inverse-time heat problem with a conformable derivative concerning the time variable. This problem is severely ill posed. A new method on the modified integral equation based on two regularization parameters is proposed to regularize this problem. Numerical results are presented to illustrate the efficiency of the proposed method.

NEUTRON DENSITY DISTRIBUTIONS IN SPHERICALLY SYMMETRIC LEAD ISOTOPES

2010 ◽  
Vol 25 (24) ◽  
pp. 2071-2076
Author(s):  
S. HADDAD
Keyword(s):  
Density Distribution ◽  
Lead Isotopes ◽  
Neutron Density ◽  
Spherically Symmetric ◽  
Fermi Model ◽  
Thomas Fermi ◽  
Density Distributions ◽  
Fermi Distribution ◽  
Neutron Density Distribution ◽  
Two Parameter

Based on a relativistic Thomas–Fermi model, it is shown that a two-parameter Fermi distribution can be used for describing the neutron density distribution in the 208 Pb nucleus.

scholarly journals Numerical Solution to Recover Time-dependent Coefficient and Free Boundary from Nonlocal and Stefan Type Overdetermination Conditions in Heat Equation

2021 ◽  
pp. 950-960
Author(s):  
Mohammed Qassim ◽  
M. S. Hussein
Keyword(s):  
Free Boundary ◽  
Heat Equation ◽  
Regularization Method ◽  
Direct Problem ◽  
Input Data ◽  
Optimization Problem ◽  
Time Dependent ◽  
Tikhonov Regularization Method ◽  
Mass Energy ◽  
Stable Solutions

This paper investigates the recovery for time-dependent coefficient and free boundary for heat equation. They are considered under mass/energy specification and Stefan conditions. The main issue with this problem is that the solution is unstable and sensitive to small contamination of noise in the input data. The Crank-Nicolson finite difference method (FDM) is utilized to solve the direct problem, whilst the inverse problem is viewed as a nonlinear optimization problem. The latter problem is solved numerically using the routine optimization toolbox lsqnonlin from MATLAB. Consequently, the Tikhonov regularization method is used in order to gain stable solutions. The results were compared with their exact solution and tested via root mean squares error (RMSE). We found that the numerical results are accurate and stable.

Multi-parameter regularization method for atmospheric remote sensing

2005 ◽  
Vol 165 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Adrian Doicu ◽  
Franz Schreier ◽  
Siegfried Hilgers ◽  
Michael Hess
Keyword(s):  
Remote Sensing ◽  
Regularization Method ◽  
Atmospheric Remote Sensing ◽  
Parameter Regularization
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