On a backward heat problem with time-dependent coefficient: Regularization and error estimates

Tuan, Nguyen Huy; Hoang, Quan Pham; Duc, Trong Dang; Minh, Triet Le

doi:10.1016/j.amc.2012.11.069

Cited by 3 publications

References 10 publications

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On regularization and error estimates for the backward heat conduction problem with time-dependent thermal diffusivity factor

Karimi

Moradlou

Hajipour

2018

Communications in Nonlinear Science and Numerical Simulation

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In this work, an accurate regularization technique based on the Meyer wavelet method is developed to solve the ill-posed backward heat conduction problem with time-dependent thermal diffusivity factor in an infinite "strip". In principle, the extremely ill-posedness of the considered problem is caused by the amplified infinitely growth in the frequency components which lead to a blow-up in the representation of the solution. Using the Meyer wavelet technique, some new stable estimates are proposed in the Hölder and Logarithmic types which are optimal in the sense of given by Tautenhahn. The stability and convergence rate of the proposed regularization technique are proved. The good performance and the high-accuracy of this technique is demonstrated through various one and two dimensional examples. Numerical simulations and some comparative results are presented.

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On regularization and error estimates for the backward heat conduction problem with time-dependent thermal diffusivity factor

Karimi

Moradlou

Hajipour

2018

Communications in Nonlinear Science and Numerical Simulation

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Automated backward error analysis for numerical code

Bai

2015

Proceedings of the 2015 ACM SIGPLAN International Conference on Object-Oriented Programming, Systems, Languages, and Applicatio

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Automated backward error analysis for numerical code

FuZhoulai

BaiZhaojun

2015

SIGPLAN Not.

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Numerical code uses floating-point arithmetic and necessarily suffers from roundoff and truncation errors. Error analysis is the process to quantify such uncertainty in the solution to a problem. Forward error analysis and backward error analysis are two popular paradigms of error analysis. Forward error analysis is more intuitive and has been explored and automated by the programming languages (PL) community. In contrast, although backward error analysis is more preferred by numerical analysts and the foundation for numerical stability, it is less known and unexplored by the PL community. To fill the gap, this paper presents an automated backward error analysis for numerical code to empower both numerical analysts and application developers. In addition, we use the computed backward error results to also compute the condition number, an important quantity recognized by numerical analysts for measuring how sensitive a function is to changes or errors in the input. Experimental results on Intel X87 FPU functions and widely-used GNU C Library functions demonstrate that our analysis is effective at analyzing the accuracy of floating-point programs.

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On a backward heat problem with time-dependent coefficient: Regularization and error estimates

Cited by 3 publications

References 10 publications

On regularization and error estimates for the backward heat conduction problem with time-dependent thermal diffusivity factor

On regularization and error estimates for the backward heat conduction problem with time-dependent thermal diffusivity factor

Automated backward error analysis for numerical code

Automated backward error analysis for numerical code

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