| 1. |
- El Fatini, Mohamed, et al.
(författare)
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A stochastic analysis for a triple delayed SIQR epidemic model with vaccination and elimination strategies
- 2020
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Ingår i: Journal of Applied Mathematics and Computing. - : Springer. - 1598-5865 .- 1865-2085. ; 64, s. 781-805
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, a delayed SIQR epidemic model with vaccination and elimination hybrid strategies is analysed under a white noise perturbation. We prove the existence and the uniqueness of a positive solution. Afterwards, we establish a stochastic threshold R-s in order to study the extinction and persistence in mean of the stochastic epidemic system. Then we investigate the existence of a stationary distribution for the delayed stochastic model. Finally, some numerical simulations are presented to support our theoretical results.
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| 2. |
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| 3. |
- Nanfuka, Mary, et al.
(författare)
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Solving the Cauchy problem for the Helmholtz equation using cubic smoothing splines
- 2022
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Ingår i: Journal of Applied Mathematics and Computing. - : Springer Berlin/Heidelberg. - 1598-5865 .- 1865-2085. ; 68:2, s. 1335-1350
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Tidskriftsartikel (refereegranskat)abstract
- We consider the Cauchy problem for the Helmholtz equation defined in a rectangular domain. The Cauchy data are prescribed on a part of the boundary and the aim is to find the solution in the entire domain. The problem occurs in applications related to acoustics and is illposed in the sense of Hadamard. In our work we consider regularizing the problem by introducing a bounded approximation of the second derivative by using Cubic smoothing splines. We derive a bound for the approximate derivative and show how to obtain stability estimates for the method. Numerical tests show that the method works well and can produce accurate results. We also demonstrate that the method can be extended to more complicated domains.
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| 4. |
- Stotsky, Alexander
(författare)
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Unified frameworks for high order Newton-Schulz and Richardson iterations: a computationally efficient toolkit for convergence rate improvement
- 2019
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Ingår i: Journal of Applied Mathematics and Computing. - : Springer Science and Business Media LLC. - 1598-5865 .- 1865-2085. ; 60:1-2, s. 605-623
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Tidskriftsartikel (refereegranskat)abstract
- Convergence rate and robustness improvement together with reduction of computational complexity are required for solving the system of linear equations in many applications such as system identification, signal and image processing, network analysis, machine learning and many others. Two unified frameworks (1) for convergence rate improvement of high order Newton-Schulz matrix inversion algorithms and (2) for combination of Richardson and iterative matrix inversion algorithms with improved convergence rate for estimation of the parameter vector are proposed. Recursive and computationally efficient version of new algorithms is developed for implementation on parallel computational units. In addition to unified description of the algorithms the frameworks include explicit transient models of estimation errors and convergence analysis. Simulation results confirm significant performance improvement of proposed algorithms in comparison with existing methods.
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