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Mathematics
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Applied Analysis and Computation
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Applied Analysis and Computation

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (28 February 2024) | Viewed by 7692

Special Issue Editor

Prof. Dr. Hongyu Liu

E-Mail Website
Guest Editor
Department of Mathematics, City University of Hong Kong, Hong Kong, China
Interests: inverse problems; wave imaging; analysis and PDEs; mathematical materials science; scattering and spectral theory; numerical analysis and scientific computing

Special Issue Information

Dear Colleagues,

Analysis and computation are powerful tools in tackling mathematical problems in science and technology. This Special Issue is dedicated to original research, as well as review-cum-expository research, that appreciates both applied analysis and computation.

Topics from inverse problems, imaging, partial differential equations, mathematical finance and economics, numerical analysis and scientific computing, and data mining and machine learning are particularly welcome.

Prof. Dr. Hongyu Liu
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Inverse problems
  • Partial differential equations
  • Mathematical finance and economics
  • Numerical analysis
  • Scientific computing
  • Applied analysis
  • Data mining and machine learning

Published Papers (4 papers)

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Research

17 pages, 338 KiB  
Article
Well-Posedness and Exponential Stability of Swelling Porous with Gurtin–Pipkin Thermoelasticity
by Tijani Abdul-Aziz Apalara and Ohud Bulayhan Almutairi
Mathematics 2022, 10(23), 4498; https://doi.org/10.3390/math10234498 - 29 Nov 2022
Cited by 9 | Viewed by 1565
Abstract
The focus of this work is to investigate the well-posedness and exponential stability of a swelling porous system with the Gurtin–Pipkin thermal effect as the only source of damping. The well-posedness result is achieved using an essential corollary to the Lumer–Phillips Theorem. By [...] Read more.
The focus of this work is to investigate the well-posedness and exponential stability of a swelling porous system with the Gurtin–Pipkin thermal effect as the only source of damping. The well-posedness result is achieved using an essential corollary to the Lumer–Phillips Theorem. By constructing a suitable Lyapunov functional, we establish an exponential stability result without the conventional limitation to the system’s parameters (coined a stability number in the literature). Generally, the study demonstrates that the unique dissipation from the Gurtin–Pipkin thermal law is sufficient to stabilize the system exponentially, irrespective of the system’s parameters. Full article
(This article belongs to the Special Issue Applied Analysis and Computation)
18 pages, 4321 KiB  
Article
Inverse Analysis for the Convergence-Confinement Method in Tunneling
by Yu-Lin Lee, Wei-Cheng Kao, Chih-Sheng Chen, Chi-Huang Ma, Pei-Wen Hsieh and Chi-Min Lee
Mathematics 2022, 10(8), 1223; https://doi.org/10.3390/math10081223 - 8 Apr 2022
Cited by 1 | Viewed by 1688
Abstract
For the safety of tunnel excavation, the observation of tunnel convergence not only provides a technique for assessing the stability of the surrounding ground, but also provides an estimate of the constitutive parameters of geological materials. This estimation method belongs to an inverse [...] Read more.
For the safety of tunnel excavation, the observation of tunnel convergence not only provides a technique for assessing the stability of the surrounding ground, but also provides an estimate of the constitutive parameters of geological materials. This estimation method belongs to an inverse algorithm process called the inverse calculation method (ICM), which utilizes the incremental concept in the convergence-confinement method (CCM) to solve the support-ground interaction of circular tunnel excavation. The method is to determine the mathematical solution of the intersection of the two nonlinear curves, the support confining curve (SCC) and the ground reaction curve (GRC) in the CCM by using Newton’s recursive method and inversely calculating the unknown parameters. To verify the validity of the developed inverse algorithm process, this study compares the results of the ICM with those of the published articles. In addition, the modulus of rock mass and unsupported span are inversely deduced using the values of convergence difference measured in the practical case of railway tunnels. Full article
(This article belongs to the Special Issue Applied Analysis and Computation)
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22 pages, 6279 KiB  
Article
Recovering Heat Source from Fourth-Order Inverse Problems by Weighted Gradient Collocation
by Judy P. Yang and Hsiang-Ming Li
Mathematics 2022, 10(2), 241; https://doi.org/10.3390/math10020241 - 13 Jan 2022
Cited by 3 | Viewed by 1121
Abstract
The weighted gradient reproducing kernel collocation method is introduced to recover the heat source described by Poisson’s equation. As it is commonly known that there is no unique solution to the inverse heat source problem, the weak solution based on a priori assumptions [...] Read more.
The weighted gradient reproducing kernel collocation method is introduced to recover the heat source described by Poisson’s equation. As it is commonly known that there is no unique solution to the inverse heat source problem, the weak solution based on a priori assumptions is considered herein. In view of the fourth-order partial differential equation (PDE) in the mathematical model, the high-order gradient reproducing kernel approximation is introduced to efficiently untangle the problem without calculating the high-order derivatives of reproducing kernel shape functions. The weights of the weighted collocation method for high-order inverse analysis are first determined. In the benchmark analysis, the unclear illustration in the literature is clarified, and the correct interpretation of numerical results is given particularly. Two mathematical formulations with four examples are provided to demonstrate the viability of the method, including the extreme cases of the limited accessible boundary. Full article
(This article belongs to the Special Issue Applied Analysis and Computation)
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12 pages, 439 KiB  
Article
A Numerical Study for the Dirichlet Problem of the Helmholtz Equation
by Yao Sun and Shijie Hao
Mathematics 2021, 9(16), 1953; https://doi.org/10.3390/math9161953 - 16 Aug 2021
Cited by 2 | Viewed by 1828
Abstract
In this paper, an effective numerical method for the Dirichlet problem connected with the Helmholtz equation is proposed. We choose a single-layer potential approach to obtain the boundary integral equation with the density function, and then we deal with the weakly singular kernel [...] Read more.
In this paper, an effective numerical method for the Dirichlet problem connected with the Helmholtz equation is proposed. We choose a single-layer potential approach to obtain the boundary integral equation with the density function, and then we deal with the weakly singular kernel of the integral equation via singular value decomposition and the Nystrom method. The direct problem with noisy data is solved using the Tikhonov regularization method, which is used to filter out the errors in the boundary condition data, although the problems under investigation are well-posed. Finally, a few examples are provided to demonstrate the effectiveness of the proposed method, including piecewise boundary curves with corners. Full article
(This article belongs to the Special Issue Applied Analysis and Computation)
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