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Mathematics
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Advances in Computational Mathematics and Applied Mathematics
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Advances in Computational Mathematics and Applied Mathematics

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

Deadline for manuscript submissions: 18 April 2025 | Viewed by 1670

Special Issue Editors

Dr. Tao Liu

E-Mail Website
Guest Editor
College of Sciences, Northeastern University, Shenyang 110819, China
Interests: deep learning; reinforcement learning; multiscale methods (multigrid and wavelet); homotopy method; inverse and Ill-posed problems; parameter reconstruction
Special Issues, Collections and Topics in MDPI journals
Dr. Fazlollah Soleymani

E-Mail Website
Guest Editor
Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan P.O. Box 45195-1159, Iran
Interests: computational finance; iterative methods; computational mathematics; stochastic differential equations
Special Issues, Collections and Topics in MDPI journals
Dr. Qiang Ma

E-Mail Website
Guest Editor
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Interests: structure-preserving algorithms for differential equations; numerical methods for stochastic differential equation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Computational mathematics and applied mathematics are two closely related, but each topic has its own emphasis in the field of mathematics. In computational mathematics, most research focuses on numerical analysis and scientific calculation methods, such as interpolation and approximation, numerical methods of differential equations, numerical integration, matrix computation, and linear equation systems. With the development of large-scale computing and parallel computing technology, computational mathematics has shown stronger capabilities in handling large-scale data and complex problems. In applied mathematics, most research focuses on practical applications in various fields, such as physics, engineering, economics, finance, geophysics, computer science, social sciences, biology, and medicine. Applied mathematics has made significant breakthroughs in optimization algorithms, data mining, and machine learning, providing strong support for the development and application of science and technology.

This Special Issue will provide a platform for researchers to share their latest advances in computational mathematics and applied mathematics, as well as their applications in solving real-world problems. We invite researchers to submit original research articles, reviews, and short communications related to the above topics. All submissions will undergo a rigorous peer-review process, and accepted papers will be published in this Special Issue of Mathematics.

Dr. Tao Liu
Dr. Fazlollah Soleymani
Prof. Dr. Qiang Ma
Guest Editors

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

  • partial differential equations
  • ordinary differential equations
  • stochastic differential equations
  • fractional differential equations
  • fractional calculus
  • inverse and ill-posed problems
  • regularization methods
  • numerical methods
  • multigrid methods
  • wavelet methods
  • homotopy methods
  • structure-preserving methods
  • artificial intelligence
  • deep learning
  • reinforcement learning
  • compact radial basis function approximations
  • approximations based on neural networks
  • node layouts for irregular domains
  • multi-asset option pricing problems
  • numerical methods for matrix functions
  • iterative methods for the solution of nonlinear equations
  • Schulz-type iterative method for generalized matrix inversion
  • biostatistics and pattern recognition
  • combination counting
  • separation theory
  • information security
  • fractional Fourier transform and its applications
  • interdisciplinary application of mathematics and other disciplines

Published Papers (4 papers)

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Research

17 pages, 648 KiB  
Article
Quasi-Analytical Solution of Kepler’s Equation as an Explicit Function of Time
by A. N. Beloiarov, V. A. Beloiarov, R. C. Cruz-Gómez, C. O. Monzón and J. L. Romero
Mathematics 2024, 12(13), 2108; https://doi.org/10.3390/math12132108 - 4 Jul 2024
Viewed by 254
Abstract
Although Kepler’s laws can be empirically proven by applying Newton’s laws to the dynamics of two particles attracted by gravitational interaction, an explicit formula for the motion as a function of time remains undefined. This paper proposes a quasi-analytical solution to address this [...] Read more.
Although Kepler’s laws can be empirically proven by applying Newton’s laws to the dynamics of two particles attracted by gravitational interaction, an explicit formula for the motion as a function of time remains undefined. This paper proposes a quasi-analytical solution to address this challenge. It approximates the real dynamics of celestial bodies with a satisfactory degree of accuracy and minimal computational cost. This problem is closely related to Kepler’s equation, as solving the equations of motion as a function of time also provides a solution to Kepler’s equation. The results are presented for each planet of the solar system, including Pluto, and the solution is compared against real orbits. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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17 pages, 357 KiB  
Article
Two Schemes of Impulsive Runge–Kutta Methods for Linear Differential Equations with Delayed Impulses
by Gui-Lai Zhang and Chao Liu
Mathematics 2024, 12(13), 2075; https://doi.org/10.3390/math12132075 - 2 Jul 2024
Viewed by 361
Abstract
In this paper, two different schemes of impulsive Runge–Kutta methods are constructed for a class of linear differential equations with delayed impulses. One scheme is convergent of order p if the corresponding Runge–Kutta method is p order. Another one in the general case [...] Read more.
In this paper, two different schemes of impulsive Runge–Kutta methods are constructed for a class of linear differential equations with delayed impulses. One scheme is convergent of order p if the corresponding Runge–Kutta method is p order. Another one in the general case is only convergent of order 1, but it is more concise and may suit for more complex differential equations with delayed impulses. Moreover, asymptotical stability conditions for the exact solution and numerical solutions are obtained, respectively. Finally, some numerical examples are provided to confirm the theoretical results. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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20 pages, 9523 KiB  
Article
Q-Sorting: An Algorithm for Reinforcement Learning Problems with Multiple Cumulative Constraints
by Jianfeng Huang, Guoqiang Lu, Yi Li and Jiajun Wu
Mathematics 2024, 12(13), 2001; https://doi.org/10.3390/math12132001 - 28 Jun 2024
Viewed by 278
Abstract
This paper proposes a method and an algorithm called Q-sorting for reinforcement learning (RL) problems with multiple cumulative constraints. The primary contribution is a mechanism for dynamically determining the focus of optimization among multiple cumulative constraints and the objective. Executed actions are picked [...] Read more.
This paper proposes a method and an algorithm called Q-sorting for reinforcement learning (RL) problems with multiple cumulative constraints. The primary contribution is a mechanism for dynamically determining the focus of optimization among multiple cumulative constraints and the objective. Executed actions are picked through a procedure with two steps: first filter out actions potentially breaking the constraints, and second sort the remaining ones according to the Q values of the focus in descending order. The algorithm was originally developed upon the classic tabular value representation and episodic setting of RL, but the idea can be extended and applied to other methods with function approximation and discounted setting. Numerical experiments are carried out on the adapted Gridworld and the motor speed synchronization problem, both with one and two cumulative constraints. Simulation results validate the effectiveness of the proposed Q-sorting in that cumulative constraints are honored both during and after the learning process. The advantages of Q-sorting are further emphasized through comparison with the method of lumped performances (LP), which takes constraints into account through weighting parameters. Q-sorting outperforms LP in both ease of use (unnecessity of trial and error to determine values of the weighting parameters) and performance consistency (6.1920 vs. 54.2635 rad/s for the standard deviation of the cumulative performance index over 10 repeated simulation runs). It has great potential for practical engineering use. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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12 pages, 629 KiB  
Article
An Efficient Iterative Approach for Hermitian Matrices Having a Fourth-Order Convergence Rate to Find the Geometric Mean
by Tao Liu, Ting Li, Malik Zaka Ullah, Abdullah Khamis Alzahrani and Stanford Shateyi
Mathematics 2024, 12(11), 1772; https://doi.org/10.3390/math12111772 - 6 Jun 2024
Viewed by 432
Abstract
The target of this work is to present a multiplication-based iterative method for two Hermitian positive definite matrices to find the geometric mean. The method is constructed via the application of the matrix sign function. It is theoretically investigated that it has fourth [...] Read more.
The target of this work is to present a multiplication-based iterative method for two Hermitian positive definite matrices to find the geometric mean. The method is constructed via the application of the matrix sign function. It is theoretically investigated that it has fourth order of convergence. The type of convergence is also discussed, which is global under an appropriate choice of the initial matrix. Numerical experiments are reported based on input matrices of different sizes as well as various stopping termination levels with comparisons to methods of the same nature and same number of matrix–matrix multiplications. The simulation results confirm the efficiency of the proposed scheme in contrast to its competitors of the same nature. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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