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Regularization of a multidimensional diffusion equation with conformable time derivative and discrete data
Author(s) -
Tuan Nguyen Huy,
Thach Tran Ngoc,
Can Nguyen Huu,
O'Regan Donal
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6133
Subject(s) - conformable matrix , mathematics , regularization (linguistics) , mathematical analysis , boundary value problem , derivative (finance) , diffusion equation , inverse problem , nonlinear system , time derivative , noisy data , algorithm , computer science , physics , economy , quantum mechanics , artificial intelligence , financial economics , economics , service (business)
In this paper, we consider a backward problem for a nonlinear diffusion equation with a conformable derivative in the case of multidimensional and discrete data. We show that this problem is ill‐posed and then we establish stable approximate solutions by two different regularization methods: the Fourier truncated method and the quasi‐boundary value (QBV) method. Furthermore, the error between the approximate solution and the sought solution is given.