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AppliedMath
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Advances in Iterative Methods and Stability Analysis for Solving Nonlinear...
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Advances in Iterative Methods and Stability Analysis for Solving Nonlinear Problems

A special issue of AppliedMath (ISSN 2673-9909). This special issue belongs to the section "Computational and Numerical Mathematics".

Deadline for manuscript submissions: 31 August 2026 | Viewed by 2972

Special Issue Editor

Dr. Chih-Wen Chang

E-Mail Website
Guest Editor
Department of Mechanical Engineering, National United University, Miaoli 360302, Taiwan
Interests: numerical analysis; forward/inverse/backward problems; spindles vibration and heat analysis; GPU/CPU computation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nonlinear problems have been investigated in science, mathematics, and engineering. Recent advancements in iterative methods have improved convergence rates and reduced computational costs, making them more efficient for complex problems.

Nonlinear problems have a wide range of applications, including mechanics, heat conduction, acoustics, semiconductors, medical imaging, nondestructive testing, physics, systems biology, finance, robotics, computer vision, radar, thermoelastics, and groundwater.

This Special Issue of AppliedMath focuses on the present mathematical theory and simulation regarding nonlinear problems and how they relate to their applications in engineering and science.

Dr. Chih-Wen Chang
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 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. AppliedMath is an international peer-reviewed open access monthly 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 1200 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

  • nonlinear problems
  • iterative methods
  • stability analysis
  • mathematical modeling
  • fractional problems
  • ordinary/partial differential equations
  • meshless methods
  • applications

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Published Papers (5 papers)

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15 pages, 297 KB  
Article
Generalized B-Curvature Tensor in Lorentzian Para-Kenmotsu Manifold with Semi-Symmetric Metric Connection
by Rajendra Prasad, Najwa Mohammed Al-Asmari, Abdul Haseeb and Sushmita Sen
AppliedMath 2026, 6(4), 52; https://doi.org/10.3390/appliedmath6040052 - 24 Mar 2026
Abstract
The main object of this work is to study the generalized B-curvature tensor in an n-dimensional Lorentzian para-Kenmotsu (briefly, (LPK)n) manifold along a semi-symmetric metric connection ∇¯. First, in an [...] Read more.
The main object of this work is to study the generalized B-curvature tensor in an n-dimensional Lorentzian para-Kenmotsu (briefly, (LPK)n) manifold along a semi-symmetric metric connection ∇¯. First, in an (LPK)n-manifold, we explore certain flatness conditions, namely, B¯(Y,Z)X=0, B¯(Y,Z)ζ=0, g(B¯(φY,φZ)φX,φW)=0, and B¯(Y,Z)·φ=0 conditions, which all result in an η-Einstein manifold. Furthermore, in an (LPK)n-manifold, we study the curvature conditions B¯.Q=0 and B¯.Q¯ = 0, which provide the scalar curvature. The generalized B-curvature tensor blends the features of different curvature tensors, allowing researchers to study conditions like semi-symmetry, pseudo-symmetry in a unified framework. Conditions like B-semi-symmetry correspond to conservation laws or stability properties in physical systems. Full article
(This article belongs to the Special Issue Advances in Iterative Methods and Stability Analysis for Solving Nonlinear Problems)
30 pages, 4512 KB  
Article
Efficient Parameter Estimation for Oscillatory Biochemical Reaction Networks via a Genetic Algorithm with Adaptive Simulation Termination
by Tatsuya Sekiguchi, Hiroyuki Hamada and Masahiro Okamoto
AppliedMath 2026, 6(3), 47; https://doi.org/10.3390/appliedmath6030047 - 16 Mar 2026
Viewed by 159
Abstract
Parameter estimation for biochemical reaction networks is computationally demanding, especially for systems with oscillatory nonlinear dynamics, where standard iterative optimization strategies, including genetic algorithms, often struggle with prohibitive computational costs. We introduce an efficient parameter estimation framework that combines a real-coded genetic algorithm [...] Read more.
Parameter estimation for biochemical reaction networks is computationally demanding, especially for systems with oscillatory nonlinear dynamics, where standard iterative optimization strategies, including genetic algorithms, often struggle with prohibitive computational costs. We introduce an efficient parameter estimation framework that combines a real-coded genetic algorithm with a novel adaptive simulation termination strategy. This strategy defines a time-dependent termination boundary based on population quantiles, which is permissive during early transients and becomes progressively stricter as simulations advance, explicitly accounting for the temporal structure of oscillatory behavior. Crucially, this mechanism facilitates the efficient identification and early simulation termination of poor parameter candidates, thus avoiding the computational expense of full-horizon simulations. The framework further integrates global exploration with the modified Powell method for rapid local refinement. Numerical experiments on two benchmark oscillatory models—the Lotka–Volterra and Goodwin oscillators—demonstrate that the framework reduces computational cost by approximately 30–50% compared to a baseline GA without this strategy. For the parameter-sensitive Goodwin model, the framework efficiently identifies candidates evolving toward damped oscillations caused by subtle parameter variations. Sensitivity analysis also confirms robustness across diverse hyperparameter settings, indicating that adaptive simulation termination provides a practical acceleration mechanism for inverse problems in systems biology where iterative objective function evaluation dominates runtime. Full article
(This article belongs to the Special Issue Advances in Iterative Methods and Stability Analysis for Solving Nonlinear Problems)
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22 pages, 797 KB  
Article
A Second-Order Nonstandard Finite Difference Method for a Malaria Propagation Model with Control
by Calisto B. Marime and Justin B. Munyakazi
AppliedMath 2026, 6(3), 36; https://doi.org/10.3390/appliedmath6030036 - 2 Mar 2026
Viewed by 218
Abstract
Standard numerical methods such as Runge–Kutta and Euler methods have been widely used to approximate solutions to nonlinear systems. These methods converge to the solution only for small step sizes; for larger time steps, they generally generate spurious or chaotic solutions. In this [...] Read more.
Standard numerical methods such as Runge–Kutta and Euler methods have been widely used to approximate solutions to nonlinear systems. These methods converge to the solution only for small step sizes; for larger time steps, they generally generate spurious or chaotic solutions. In this paper, we consider a malaria propagation model with control for which we construct a second-order nonstandard finite difference scheme that preserves the important mathematical properties of the continuous model, which are positivity, boundedness, and stability of solutions irrespective of the step size. Moreover, we show that the equilibrium points of the discrete model are the same as those of the continuous model. By applying the double mesh principle, we provide evidence that the second-order NSFD scheme approximates the true solution with small errors. Theoretical assertions and numerical results show the advantages of the developed second-order nonstandard finite difference method. Full article
(This article belongs to the Special Issue Advances in Iterative Methods and Stability Analysis for Solving Nonlinear Problems)
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9 pages, 348 KB  
Article
A Two-Stage Numerical Algorithm for the Simultaneous Extraction of All Zeros of Meromorphic Functions
by Ivan K. Ivanov and Stoil I. Ivanov
AppliedMath 2025, 5(4), 138; https://doi.org/10.3390/appliedmath5040138 - 6 Oct 2025
Viewed by 672
Abstract
In this paper, we present an effective two-stage numerical algorithm for the simultaneous finding of all roots of meromorphic functions in a region within the complex plane. At the first stage, we construct a polynomial with the same roots as the ones of [...] Read more.
In this paper, we present an effective two-stage numerical algorithm for the simultaneous finding of all roots of meromorphic functions in a region within the complex plane. At the first stage, we construct a polynomial with the same roots as the ones of the considered function; at the next step, we apply some method for the simultaneous approximation of its roots. To show the efficiency and applicability of our algorithm together with its advantages over the classical Newton, Halley and Chebyshev’s iterative methods, we conduct three numerical examples, where we apply it to two test functions and to an important engineering problem. Full article
(This article belongs to the Special Issue Advances in Iterative Methods and Stability Analysis for Solving Nonlinear Problems)
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14 pages, 268 KB  
Article
Ricci–Yamabe Solitons on Sasakian Manifolds with the Generalized Tanaka–Webster Connection
by Abdul Haseeb
AppliedMath 2025, 5(1), 22; https://doi.org/10.3390/appliedmath5010022 - 3 Mar 2025
Cited by 1 | Viewed by 1012
Abstract
In this article, we analyze some curvature restrictions satisfying by the concircular curvature tensor in (2n+1)-dimensional Sasakian manifolds with the generalized Tanaka–Webster connection ∇¯ admitting Ricci–Yamabe solitons. Finally, we give an example of three-dimensional Sasakian manifolds [...] Read more.
In this article, we analyze some curvature restrictions satisfying by the concircular curvature tensor in (2n+1)-dimensional Sasakian manifolds with the generalized Tanaka–Webster connection ∇¯ admitting Ricci–Yamabe solitons. Finally, we give an example of three-dimensional Sasakian manifolds which verifies some of our findings. Full article
(This article belongs to the Special Issue Advances in Iterative Methods and Stability Analysis for Solving Nonlinear Problems)
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