Advances in Computational Mathematics and Applied Mathematics, 2nd Edition

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

Deadline for manuscript submissions: 31 March 2026 | Viewed by 1542

Special Issue Editors

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
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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

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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
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Special Issue Information

Dear Colleagues,

This Special Issue is a continuation of our previous Special Issue, entitled “Advances in Computational Mathematics and Applied Mathematics”. Computational mathematics and applied mathematics are two closely related fields, each with its emphasis within the realm of mathematics. In computational mathematics, most research focuses on numerical analysis and scientific calculation methods, including interpolation and approximation, numerical methods for 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 topics mentioned above. 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
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 250 words) can be sent to the Editorial Office for assessment.

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

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Related Special Issue

Published Papers (3 papers)

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Research

26 pages, 2334 KB  
Article
Nonlinear Optical Characteristics of Copper Oxide Thin Films Interpreted Through Soliton Solutions of the Convective–Diffusive Cahn–Hilliard Equation
by Nan Xing, Umair Asghar, Khaleel Ahmad and Luminita-Ioana Cotirla
Mathematics 2025, 13(23), 3799; https://doi.org/10.3390/math13233799 - 26 Nov 2025
Viewed by 131
Abstract
This study investigates the convective–diffusive Cahn–Hilliard equation, a nonlinear model which is used in real-world applications to phase separation and material pattern formation. Using the modified Sardar sub-problem technique, which is an extension of the Sardar sub-equation approach, we derive multiple classes of [...] Read more.
This study investigates the convective–diffusive Cahn–Hilliard equation, a nonlinear model which is used in real-world applications to phase separation and material pattern formation. Using the modified Sardar sub-problem technique, which is an extension of the Sardar sub-equation approach, we derive multiple classes of exact soliton solutions, including bright, dark, kink, and periodic forms. The parametric behaviors of these solutions are examined and visualized through analytical plots generated in Mathematica and Maple. Furthermore, UV–Vis spectrophotometry is employed to examine the optical response of copper oxide (CuO) thin films. The films exhibited a sharp absorption edge around 380–410 nm and an optical band gap of approximately 2.3 eV, confirming their semiconducting nature. The experimentally observed periodic transmission characteristics are linked with the theoretical soliton profiles predicted by the model. Overall, the proposed analytical and experimental framework establishes a clear connection between nonlinear wave theory and thin-film optical characterization, providing new insights into soliton transformation phenomena in complex material systems. Full article
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20 pages, 4034 KB  
Article
Preserving Multiple Conserved Quantities of Stochastic Differential Equations via Projection Technique
by Xuliang Li, Zhenyu Wang and Xiaohua Ding
Mathematics 2025, 13(22), 3614; https://doi.org/10.3390/math13223614 - 11 Nov 2025
Viewed by 359
Abstract
Stochastic differential equations (SDEs) with multiple conserved quantities are ubiquitous in scientific fields, modeling systems from molecular dynamics to celestial mechanics. While geometric numerical integrators that preserve single invariants are well-established, constructing efficient and high-order numerical schemes for SDEs with multiple conserved quantities [...] Read more.
Stochastic differential equations (SDEs) with multiple conserved quantities are ubiquitous in scientific fields, modeling systems from molecular dynamics to celestial mechanics. While geometric numerical integrators that preserve single invariants are well-established, constructing efficient and high-order numerical schemes for SDEs with multiple conserved quantities remains a challenge. Existing approaches often suffer from high computational costs or lack desirable numerical properties like symmetry. This paper introduces two novel classes of projection-based numerical methods tailored for SDEs with multiple conserved quantities. The first method projects the increments of an underlying numerical scheme onto a discrete tangent space, ensuring all invariants are preserved by construction. The second method leverages a local coordinates approach, transforming the SDE onto the manifold defined by the invariants, solving it numerically, and then projecting back, guaranteeing the solution evolves on the correct manifold. We prove that both methods inherit the mean-square convergence order of their underlying schemes. Furthermore, we propose a simplified strategy that reduces computational expense by redefining the multiple invariants into a single one, offering a practical trade-off between exact preservation and efficiency. Numerical experiments confirm the theoretical findings and demonstrate the superior efficiency and structure-preserving capabilities of our methods. Full article
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15 pages, 595 KB  
Article
A Sixth-Order Iterative Scheme Through Weighted Rational Approximations for Computing the Matrix Sign Function
by Ce Zhang, Bo Zhao, Wenjing Ren, Ruosong Cao and Tao Liu
Mathematics 2025, 13(17), 2849; https://doi.org/10.3390/math13172849 - 4 Sep 2025
Viewed by 688
Abstract
This work introduces a sixth-order multi-step iterative algorithm for obtaining the matrix sign function of nonsingular matrices. The presented methodology employs optimized rational approximations combined with strategically formulated weight functions to achieve both computational efficiency and numerical precision. We present a convergence study [...] Read more.
This work introduces a sixth-order multi-step iterative algorithm for obtaining the matrix sign function of nonsingular matrices. The presented methodology employs optimized rational approximations combined with strategically formulated weight functions to achieve both computational efficiency and numerical precision. We present a convergence study that includes the analytical derivation of error terms, formally proving the sixth-order convergence characteristics. Numerical simulations substantiate the theoretical results and demonstrate the algorithm’s advantage over current state-of-the-art approaches in terms of both accuracy and computational performance. Full article
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