The First-Order Coefficient of the Second Order Parabolic Equation for Numerical Reconstruction

2018 4th International Conference on Environmental Science and Material Application

生态环境科学;材料科学

Ren, Jianlong^1 ; Zhang, Tainian^1 ; Zeng, Jian^1

Lan Zhou Jiao Tong University, Lan Zhou

730070, China^1

关键词: Finite difference scheme;    Numerical algorithms;    Numerical experiments;    Numerical reconstruction;    Numerical results;    Numerical solution;    Optimal control frameworks;    Second-order parabolic equations;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/252/3/032132/pdf
DOI  :  10.1088/1755-1315/252/3/032132

来源: IOP

【 摘 要 】

This paper investigates an inverse problem of using the additional conditions to reconstruct the first-order coefficient of the second order parabolic equation. Based on the optimal control framework, the existence of the minimize of the cost functional is proved, and the necessary condition which must be satisfied by the minimize is deduced. In the process of computation of the forward problem, a discrete finite difference scheme is constructed and the chasing method is applied to calculate the numerical solution. Finally, a numerical algorithm on the basis of the Gradient iterative method is designed to treat the inverse problem and some numerical experiments are also performed. The numerical results show that the algorithm designed in this paper is stable and that the coefficient is recovered very well.