In this article, the application of discrete mollification as a regularization procedure for solving a nonlinear inverse problem in one dimensional space is considered. Illposedness is identified as one of the main characteristics of inverse problems. It is clear that if we have a noisy data, the inverse problem becomes unstable. As such, a numerical procedure based on discrete mollification and space marching method is applied to address the ill-posedness of the mentioned problem. The regularization parameter is selected by generalized cross validation (GCV) method. The numerical stability and convergence of the proposed method are investigated. Finally, some test problems, whose exact solutions are known, are solved using this method to show the efficiency.
Bodaghi, S., Zakeri, A., & Amiraslani, A. (2021). Regularization of a nonlinear inverse problem by discrete mollification method. Computational Methods for Differential Equations, 9(1), 313-326. doi: 10.22034/cmde.2020.30808.1461
MLA
Soheila Bodaghi; Ali Zakeri; Amir Amiraslani. "Regularization of a nonlinear inverse problem by discrete mollification method". Computational Methods for Differential Equations, 9, 1, 2021, 313-326. doi: 10.22034/cmde.2020.30808.1461
HARVARD
Bodaghi, S., Zakeri, A., Amiraslani, A. (2021). 'Regularization of a nonlinear inverse problem by discrete mollification method', Computational Methods for Differential Equations, 9(1), pp. 313-326. doi: 10.22034/cmde.2020.30808.1461
VANCOUVER
Bodaghi, S., Zakeri, A., Amiraslani, A. Regularization of a nonlinear inverse problem by discrete mollification method. Computational Methods for Differential Equations, 2021; 9(1): 313-326. doi: 10.22034/cmde.2020.30808.1461
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