Parameter Estimation for a Type of Fractional Diffusion Equation Based on Compact Difference Scheme

Gu, Wei; Wei, Fang; Li, Min

doi:10.3390/sym14030560

Cited by 4 publications

(1 citation statement)

References 39 publications

(40 reference statements)

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“…The direct problems for the time-fractional diffusion equation have been studied for many years, for example, the maximum principle, uniqueness results, existence results, numerical solutions, and analytic solutions [9][10][11][12][13][14][15][16][17]. In addition, various inverse problems of fractional diffusion equations have been researched extensively, such as inverse source problems [18,19], backward problems [20,21], the Cauchy problem [22,23], the inversion for parameter, or fractional order [24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Recovering a Space-Dependent Source Term in the Fractional Diffusion Equation with the Riemann–Liouville Derivative

Liu¹

2022

Mathematics

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This research determines an unknown source term in the fractional diffusion equation with the Riemann–Liouville derivative. This problem is ill-posed. Conditional stability for the inverse source problem can be given. Further, a fractional Tikhonov regularization method was applied to regularize the inverse source problem. In the theoretical results, we propose a priori and a posteriori regularization parameter choice rules and obtain the convergence estimates.

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Section: Introductionmentioning

confidence: 99%

Recovering a Space-Dependent Source Term in the Fractional Diffusion Equation with the Riemann–Liouville Derivative

Liu¹

2022

Mathematics

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Unbiased Identification of Fractional Order System with Unknown Time-Delay Using Bias Compensation Method

2022

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In the field of engineering, time-delay is a typical occurrence. In reality, the inner dynamics of many industrial processes are impacted by delay or after-effect events. This paper discusses the identification of continuous-time fractional order system with unknown time-delay using the bias compensated least squares algorithm. The basic concept is to remove the imposed bias by including a correction term into the least squares estimations. The suggested approach makes a significant contribution by the estimation, iteratively, of fractional order system coefficients as well as the orders and the time-delay using a nonlinear optimization algorithm. The main advantage of this method is to provide a simple and powerful algorithm with good accuracy. The suggest method performances are assessed through two numerical examples.

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Damage Effectiveness Calculation of Hitting Targets with Ammunition Based on Bayesian Multinomial Distribution

Liu

Shi

2022

Symmetry

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Owning to the fact that ammunition can cause varying degrees of damage to its target, this article presents a damage effectiveness calculation method of hitting targets with ammunition based on Bayesian multinomial distribution to solve the problems of complex processes, few trial times and difficult calculations of damage probability in target-hitting tests with high-tech ammunition, according to a calculation index of damage effectiveness about the occurrence probability of different damage. Based on the concept of symmetry, the idea of “divide damage level—determine distribution—integrate information—solve distribution” is adopted. Firstly, this paper describes the damage effectiveness test of ammunition attacking targets with multiple distributions; secondly, this paper integrates the damage effectiveness information of ammunition strike targets with Dempster–Shafer evidence theory (D–S evidence theory) and symmetry advantage; finally, this paper attempts to solve the symmetric posterior distribution of damage effectiveness parameters with Bayesian theory and the Markov chain Monte Carlo (MCMC) method. The result demonstrates that this method is very significant in improving the calculation accuracy of ammunition damage effectiveness, which could describe the damage effectiveness of ammunition in detail by integrating the prior information with multiple types of damage effectiveness.

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Parameter Estimation for a Type of Fractional Diffusion Equation Based on Compact Difference Scheme

Cited by 4 publications

References 39 publications

Recovering a Space-Dependent Source Term in the Fractional Diffusion Equation with the Riemann–Liouville Derivative

Recovering a Space-Dependent Source Term in the Fractional Diffusion Equation with the Riemann–Liouville Derivative

Unbiased Identification of Fractional Order System with Unknown Time-Delay Using Bias Compensation Method

Damage Effectiveness Calculation of Hitting Targets with Ammunition Based on Bayesian Multinomial Distribution

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