Results 191 to 200 of about 287 (213)
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A Jacobi spectral method for calculating fractional derivative based on mollification regularization
Asymptotic Analysis, 2023In this article, we construct a Jacobi spectral collocation scheme to approximate the Caputo fractional derivative based on Jacobi–Gauss quadrature. The convergence analysis is provided in anisotropic Jacobi-weighted Sobolev spaces. Furthermore, the convergence rate is presented for solving Caputo fractional derivative with noisy data by invoking the ...
Zhang, Wen +3 more
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A New Mollification Method for Numerical Differentiation of 2D Periodic Functions
2009 International Joint Conference on Computational Sciences and Optimization, 2009In this paper, we present a new method for numerical differentiation of bivariate periodic functions when a set of noisy data is given. TSVD is chosen as the needed regularization technique. It turns out the new method coincides with some type of truncated Fourier series approach. A numerical example is also given to show the efficiency of the method.
Zhenyu Zhao +3 more
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Some Applications of the Mollification Method
2001The Mollification Method is a filtering procedure that is appropriate for the regularization of a variety of ill-posed problems. In this review, we briefly introduce the method, including its main feature, which is its ability to automatically select regularization parameters.
C. E. Mejía, D. A. Murio, S. Zhan
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A mollification regularization method for unknown source in time-fractional diffusion equation
International Journal of Computer Mathematics, 2014In the present paper, we consider an inverse source problem for a fractional diffusion equation. This problem is ill-posed, i.e. the solution (if it exists) does not depend continuously on the data. We give the mollification regularization method to solve this problem.
Fan Yang 0026, Chu-Li Fu, Xiao-Xiao Li
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Determining an Unknown Source in the Heat Equation by a Mollification Regularization Method
2010 International Conference on Computational Intelligence and Software Engineering, 2010The problem of identifying an unknown source in the heat equation is ill-posed in the sense that the solution(if it exists) does not depend continuously on the data. In this paper, we proposed a regularization strategy-mollification method to analysis the stability of the problem. Meanwhile, we proposed numerical implement.
Ailin Qian, Yongxin Gui
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A mollification regularization method for identifying the time-dependent heat source problem
Journal of Engineering Mathematics, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yang, Fan, Fu, Chu-Li, Li, Xiao-Xiao
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The Smoothing of Temperature Data Using the Mollification Method in Heat Flux Estimating
Numerical Heat Transfer, Part A: Applications, 2010This article proposes a procedure to mollify the temperature data prior to utilizing the inverse heat conduction problem methods for unknown heat flux estimation. The measured transient temperature data may be obtained from locations inside the body or on its inactive boundaries.
F. Kowsary, S. D. Farahani
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An a posteriori mollification method for the heat equation backward in time
Journal of Inverse and Ill-posed Problems, 2016Abstract The heat equation backward in time u t
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International Journal of Wavelets, Multiresolution and Information Processing, 2019
In this paper, the ill-posed Cauchy problem for the Helmholtz equation is investigated in a strip domain. To obtain stable numerical solution, a mollification regularization method with Dirichlet kernel is proposed. Error estimate between the exact solution and its approximation is given.
Shangqin He, Xiufang Feng
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In this paper, the ill-posed Cauchy problem for the Helmholtz equation is investigated in a strip domain. To obtain stable numerical solution, a mollification regularization method with Dirichlet kernel is proposed. Error estimate between the exact solution and its approximation is given.
Shangqin He, Xiufang Feng
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Regularization of a nonlinear inverse problem by discrete mollification method
2021Summary: 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.
Bodaghi, Soheila +2 more
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