A spectral element method for solving backward parabolic problems
S Moazzezi, AH Salehi Shayegan… - International Journal for …, 2018 - Taylor & Francis
S Moazzezi, AH Salehi Shayegan, A Zakeri
International Journal for Computational Methods in Engineering Science …, 2018•Taylor & FrancisIn this article, some existence and uniqueness theorems for a quasisolution of backward
parabolic problems are given. A computational algorithm to find the quasisolution is also
provided. In this algorithm, in order to approximate the quasisolution, spectral element
method is used. Since the obtained system of linear equations is ill-conditioned, we apply
the Levenberg–Marquardt regularization. Finally, some numerical examples are given to
show the efficiency and accuracy of the introduced method.
parabolic problems are given. A computational algorithm to find the quasisolution is also
provided. In this algorithm, in order to approximate the quasisolution, spectral element
method is used. Since the obtained system of linear equations is ill-conditioned, we apply
the Levenberg–Marquardt regularization. Finally, some numerical examples are given to
show the efficiency and accuracy of the introduced method.
Abstract
In this article, some existence and uniqueness theorems for a quasisolution of backward parabolic problems are given. A computational algorithm to find the quasisolution is also provided. In this algorithm, in order to approximate the quasisolution, spectral element method is used. Since the obtained system of linear equations is ill-conditioned, we apply the Levenberg–Marquardt regularization. Finally, some numerical examples are given to show the efficiency and accuracy of the introduced method.
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