A Haar wavelet-based scheme for finding the control parameter in nonlinear inverse heat conduction equation

Open Physics

卷:19

Ahmed Hijaz¹  Ahmad Masood¹  Nisar Muhammad²  Liu Xuan³  Ahmad Imtiaz⁴  Ahsan Muhammad⁴  Lin Shanwei⁵ 

[1] Department of Basic Sciences, University of Engineering and Technology Peshawar, Peshawar, Pakistan;

[2] Department of Mathematics and Statistics, Macquarie University, Sydney, Australia;

[3] Department of Mathematics, Hanshan Normal University, Chaozhou, 515041, China;

[4] Department of Mathematics, University of Swabi, Khyber Pakhtunkhwa 23200, Pakistan;

[5] School of Economics and Management, Hanshan Normal University, Chaozhou, 515041, China;

关键词: nonlinear ill-posed pde;    haar wavelets;    stability;    condition number;   

DOI  :  10.1515/phys-2021-0080

来源: DOAJ

【 摘 要 】

In this article, a hybrid Haar wavelet collocation method (HWCM) is proposed for the ill-posed inverse problem with unknown source control parameters. Applying numerical techniques to such problems is a challenging task due to the presence of nonlinear terms, unknown control parameter sources along the solution inside the given region. To find the numerical solution, derivatives are discretized adopting implicit finite-difference scheme and Haar wavelets. The computational stability and theoretical rate of convergence of the proposed HWCM are discussed in detail. Two numerical experiments are incorporated to show the well-condition behavior of the matrix obtained from HWCM and hence not required to supplement some regularization procedures. Moreover, the numerical solutions of the considered experiments illustrate the reliability, suitability, and correctness of HWCM.

【 授权许可】

Unknown