Article
Mathematics
Ahmed AlGhamdi, Omar Bazighifan, Rami Ahmad El-Nabulsi
Summary: This article establishes new oscillation theorems for fourth-order differential equations, utilizing the Riccati technique and the integral averaging technique. Multiple practical examples are provided as proof of the effectiveness of the new criteria.
Article
Mathematics, Applied
Musa Cakmak
Summary: In this study, a collocation method based on Fibonacci polynomials is used to approximately solve a class of nonlinear pantograph differential equations. The unknown coefficients of the approximate solution function are calculated through a nonlinear algebraic system obtained via collocation points. The proposed method is validated by testing its performance using absolute error functions and comparing the results with exact solutions and other existing methods in literature.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Multidisciplinary Sciences
D. A. Refaai, M. M. A. El-Sheikh, Gamal A. F. Ismail, Mohammed Zakarya, Ghada AlNemer, Haytham M. Rezk
Summary: This article discusses several forms of Ulam stability of nonlinear fractional delay differential equations. The investigation is based on a generalised Gronwall's inequality and Picard operator theory. Implementations are provided to demonstrate the stability results obtained for finite intervals.
Article
Business, Finance
Weiwei Li, Prasad Padmanabhan, Chia-Hsing Huang
Summary: This study examines the relationships between ESG scores and debt structure, finding a U-shaped relationship between ESG composite scores and long-term debt. The study also reveals that ESG has a stronger effect on long-term debt in polluting industries and when economic policy uncertainty is low. Additionally, ESG activities have long-term effects on debt maturity, and there is an inverse U-shaped relationship between ESG scores and cost of debt.
INTERNATIONAL REVIEW OF FINANCIAL ANALYSIS
(2024)
Article
Business, Finance
Chao-Hsi Huang, Yi-Shan Hsieh
Summary: The study examines the leverage dynamics of publicly listed and unlisted firms in Taiwan from 1986 to 2014, finding that debt and equity financing tend to move in line with the business cycle for most firms. Different patterns of leverage dynamics were observed for mature and less mature firms, with larger publicly listed firms showing procyclical leverage while smaller unlisted firms exhibiting countercyclical leverage. These findings align with the financial growth cycle hypothesis and suggest that small and medium enterprises in Taiwan are unlikely to contribute to over-leveraging and financial instability.
INTERNATIONAL REVIEW OF ECONOMICS & FINANCE
(2021)
Article
Multidisciplinary Sciences
David S. Glass, Xiaofan Jin, Ingmar H. Riedel-Kruse
Summary: Studying biological networks through delay differential equation models provides important insights, such as parameter reduction, analytical relationships between ODE and DDE models, phase space for autoregulation, behaviors of feedforward loops, and a unified Hill-function logic framework. Explicit-delay modeling simplifies the phenomenology of biological networks and may aid in discovering new functional motifs.
NATURE COMMUNICATIONS
(2021)
Article
Automation & Control Systems
Junhao Hu, Wei Mao, Xuerong Mao
Summary: This paper studies a class of highly nonlinear hybrid stochastic differential delay equations (SDDEs). Unlike most existing papers, the time delay functions in the SDDEs are no longer required to be differentiable, let alone have derivatives less than 1. Generalized Hasminskii-type theorems are established for the existence and uniqueness of global solutions. Compared with existing results, our new theorems are more general and can be applied to a wider class of highly nonlinear SDDEs. Further sufficient conditions are obtained for asymptotic boundedness and stability. (c) 2022 Elsevier Ltd. All rights reserved.
Article
Mathematics, Interdisciplinary Applications
Hail S. Alrashdi, Osama Moaaz, Ghada AlNemer, Elmetwally M. Elabbasy
Summary: We present simplified criteria for evaluating the oscillatory behavior of solutions to a class of higher-order functional differential equations in the non-canonical case. By using a comparison approach with first-order equations that have standard oscillation criteria, we provide a two-condition criteria without checking the additional conditions. Finally, we present examples to illustrate the significance of the findings.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Somayeh Nemati, Zahra Rezaei Kalansara
Summary: This work proposes a low-cost spectral method based on modified hat functions to solve fractional delay differential equations. By utilizing the properties of basis functions, Caputo derivative, and Riemann-Liouville fractional integral, the main problem is transformed into systems of nonlinear algebraic equations, yielding approximate solutions. Error analysis demonstrates the convergence order of the method, and its validity and accuracy are verified through application to sample problems.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics
Md. Habibur Rahman, Muhammad I. Bhatti, Nicholas Dimakis
Summary: In this paper, a novel technique for solving nonlinear multidimensional fractional differential equations was proposed using a modified version of the Bernstein polynomials called the Bhatti-fractional polynomials. The method approximated the desired solution and treated the resulting equation as a matrix equation. Experimental results showed higher accuracy and computational efficiency, making it suitable for solving fractional differential equations in various programming languages.
Article
Mathematics, Applied
Rui Zhan, Jinwei Fang
Summary: In this work, we extend previous research on exponential integrators to nonlinear stiff delay differential equations. We address the challenges of handling nonlinear and delay terms, and propose linearization and interpolation techniques to reduce the number of stiff order conditions. We construct high-order exponential Rosenbrock methods and analyze their convergence.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
N. A. Elkot, E. H. Doha, I. G. Ameen, A. S. Hendy, M. A. Zaky
Summary: This work studies a spectral collocation approach for fractional nonlinear pantograph delay differential equations with nonsmooth solutions. By matching the singularity in the solution and maximizing the convergence rate, an auxiliary transformation is adapted to improve the regularity of the resulting equation, achieving spectral accuracy. The spectral convergence rate is discussed in the weighted L2-norm and the L infinity-norm, and numerical results are provided to confirm the theoretical analysis.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Xiaoqiang Yan, Xu Qian, Hong Zhang, Songhe Song
Summary: This paper focuses on numerical solutions of nonlinear delay-differential-algebraic equations with proportional delay, which are transformed into equations with constant delay through exponential transformation. The unique solvability, convergence, and stability of block boundary value methods for solving this type of equations are rigorously proved, and their computational effectiveness and theoretical correctness are illustrated through numerical examples.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Tyler Cassidy
Summary: This study explores the equivalence of compartmental models with nonlinear transit rates and possibly delayed arguments to a scalar distributed DDE. By calculating equilibria and characteristic functions, the practical utility of these equivalences is demonstrated. The DDE formulation is used to uncover physiological processes hidden within the compartmental structure of the ODE model.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2021)
Article
Mathematics
R. A. Sallam, M. M. A. El-Sheikh, E. El-Saedy
Summary: This paper examines a class of second-order neutral delay differential equations and establishes new oscillation criteria to complement and improve existing results. Two examples are provided to support the findings.
MATHEMATICA SLOVACA
(2021)
Article
Mathematics, Applied
Gabriel J. Lord, Antoine Tambue
APPLIED NUMERICAL MATHEMATICS
(2019)
Article
Economics
Rock Stephane Koffi, Antoine Tambue
COMPUTATIONAL ECONOMICS
(2020)
Article
Mathematics, Applied
Jean Daniel Mukam, Antoine Tambue
APPLIED NUMERICAL MATHEMATICS
(2020)
Article
Statistics & Probability
Jean Daniel Mukam, Antoine Tambue
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2020)
Article
Mathematics
Antoine Tambue, Jean Daniel Mukam
INDAGATIONES MATHEMATICAE-NEW SERIES
(2020)
Article
Mathematics, Applied
Aurelien Junior Noupelah, Antoine Tambue
Summary: This paper explores the numerical approximation of a general second order semilinear stochastic partial differential equation driven by a fractional Brownian motion and Poisson random measure. The study achieves optimal strong convergence rates using three time-stepping methods and reveals the effectiveness of the theoretical results through numerical experiments.
NUMERICAL ALGORITHMS
(2021)
Article
Mathematics, Applied
David Sena Attipoe, Antoine Tambue
Summary: This paper introduces two novel numerical spatial discretization techniques for a degenerated partial differential equation (PDE) in one dimension, based on the mimetic finite difference method. A fitted mimetic finite difference scheme is proposed to handle the degeneracy of the PDE, along with the standard method. Theoretical results are validated through numerical experiments, showing the superiority of the new schemes in accuracy compared to standard methods.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Antoine Tambue, Jean Daniel Mukam
Summary: This paper investigates the numerical approximation of stochastic convection-reaction-diffusion equations using two explicit exponential integrators, achieving higher convergence orders with the construction of accelerated numerical methods. Numerical experiments are provided to illustrate the theoretical results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Economics
Christelle Dleuna Nyoumbi, Antoine Tambue
Summary: This paper introduces a novel fitted finite volume method to solve high dimensional degenerated HJB equation, which is challenging due to the coupling of the degenerated second-order partial differential equation with an optimization problem. The matrices resulting from spatial discretization and temporal discretization are M-matrices.
COMPUTATIONAL ECONOMICS
(2023)
Article
Economics
Rock Stephane Koffi, Antoine Tambue
Summary: In this paper, a special finite volume method called Multi-Point Flux Approximation method (MPFA) is introduced for pricing European and American options in a two dimensional domain. By combining the L-MPFA method with the fitted finite volume method to tackle the degeneracy of the Black-Scholes operator, a novel scheme called the fitted L-MPFA method is proposed. Numerical experiments demonstrate the accuracy of this novel method compared to well known schemes for pricing options.
COMPUTATIONAL ECONOMICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Bawfeh K. Kometa, Antoine Tambue, Naveed Iqbal
Summary: This article presents a new class of semi-Lagrangian methods for the numerical approximation of hyperbolic conservation laws. The methods combine the advantages of SLDG methods and RKDG methods, resulting in high-order accuracy and local conservative properties, suitable for convection-dominated convection-diffusion problems.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2022)
Article
Mathematics, Applied
David Sena Attipoe, Antoine Tambue
Summary: This paper proposes novel numerical techniques based on mimetic finite difference method for accurately pricing European and American options. The techniques preserve and conserve general properties of the continuum operator in the discrete case and further handle the degeneracy of the underlying partial differential equations (PDE).
RESULTS IN APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Christelle Dleuna Nyoumbi, Antoine Tambue
Summary: This article introduces a numerical method based on the fitted finite volume method to approximate the HJB equation in stochastic optimal control problems in one and two dimensional domains. By discretizing the HJB equation and using the Implicit Euler method for time discretization, the degeneracy of the equation is successfully addressed. Numerical results demonstrate the robustness of the fitted finite volume numerical method compared to the standard finite difference method.
Article
Mathematics, Applied
Antoine Tambue, Jean Daniel Mukam
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2020)
Article
Mathematics, Applied
Antoine Tambue, Jean Daniel Mukam
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
(2019)
Article
Mathematics, Applied
Hao Liu, Yuzhe Li
Summary: This paper investigates the finite-time stealthy covert attack on reference tracking systems with unknown-but-bounded noises. It proposes a novel finite-time covert attack method that can steer the system state into a target set within a finite time interval while being undetectable.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Nikolay A. Kudryashov, Aleksandr A. Kutukov, Sofia F. Lavrova
Summary: The Chavy-Waddy-Kolokolnikov model with dispersion is analyzed, and new properties of the model are studied. It is shown that dispersion can be used as a control mechanism for bacterial colonies.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Qiang Ma, Jianxin Lv, Lin Bi
Summary: This paper introduces a linear stability equation based on the Boltzmann equation and establishes the relationship between small perturbations and macroscopic variables. The numerical solutions of the linear stability equations based on the Boltzmann equation and the Navier-Stokes equations are the same under the continuum assumption, providing a theoretical foundation for stability research.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Samuel W. Akingbade, Marian Gidea, Matteo Manzi, Vahid Nateghi
Summary: This paper presents a heuristic argument for the capacity of Topological Data Analysis (TDA) to detect critical transitions in financial time series. The argument is based on the Log-Periodic Power Law Singularity (LPPLS) model, which characterizes financial bubbles as super-exponential growth (or decay) with increasing oscillations approaching a tipping point. The study shows that whenever the LPPLS model fits the data, TDA generates early warning signals. As an application, the approach is illustrated using positive and negative bubbles in the Bitcoin historical price.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Xavier Antoine, Jeremie Gaidamour, Emmanuel Lorin
Summary: This paper is interested in computing the ground state of nonlinear Schrodinger/Gross-Pitaevskii equations using gradient flow type methods. The authors derived and analyzed Fractional Normalized Gradient Flow methods, which involve fractional derivatives and generalize the well-known Normalized Gradient Flow method proposed by Bao and Du in 2004. Several experiments are proposed to illustrate the convergence properties of the developed algorithms.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Lianwen Wang, Xingyu Wang, Zhijun Liu, Yating Wang
Summary: This contribution presents a delayed diffusive SEIVS epidemic model that can predict and quantify the transmission dynamics of slowly progressive diseases. The model is applied to fit pulmonary tuberculosis case data in China and provides predictions of its spread trend and effectiveness of interventions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Shuangxi Huang, Feng-Fei Jin
Summary: This paper investigates the error feedback regulator problem for a 1-D wave equation with velocity recirculation. By introducing an invertible transformation and an adaptive error-based observer, an observer-based error feedback controller is constructed to regulate the tracking error to zero asymptotically and ensure bounded internal signals.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Weimin Liu, Shiqi Gao, Feng Xu, Yandong Zhao, Yuanqing Xia, Jinkun Liu
Summary: This paper studies the modeling and consensus control of flexible wings with bending and torsion deformation, considering the vibration suppression as well. Unlike most existing multi-agent control theories, the agent system in this study is a distributed parameter system. By considering the mutual coupling between the wing's deformation and rotation angle, the dynamics model of each agent is expressed using sets of partial differential equations (PDEs) and ordinary differential equations (ODEs). Boundary control algorithms are designed to achieve control objectives, and it is proven that the closed-loop system is asymptotically stable. Numerical simulation is conducted to demonstrate the effectiveness of the proposed control scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Gourav Mandal, Lakshmi Narayan Guin, Santabrata Chakravarty
Summary: The ecological framework investigates the dynamical complexity of a system influenced by prey refuge and alternative food sources for predators. This study provides a thorough investigation of the stability-instability phenomena, system parameters sensitivity, and the occurrence of bifurcations. The bubbling phenomenon, which indicates a change in the amplitudes of successive cycles, is observed in the current two-dimensional continuous system. The controlling system parameter for the bubbling phenomena is found to be the most sensitive. The prediction and identification of bifurcations in the dynamical system are crucial for theoretical and field researchers.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Damian Trofimowicz, Tomasz P. Stefanski, Jacek Gulgowski, Tomasz Talaska
Summary: This paper presents the application of control engineering methods in modeling and simulating signal propagation in time-fractional electrodynamics. By simulating signal propagation in electromagnetic media using Maxwell's equations with fractional-order constitutive relations in the time domain, the equations in time-fractional electrodynamics can be considered as a continuous-time system of state-space equations in control engineering. Analytical solutions are derived for electromagnetic-wave propagation in the time-fractional media based on state-transition matrices, and discrete time zero-order-hold equivalent models are developed and their analytical solutions are derived. The proposed models yield the same results as other reference methods, but are more flexible in terms of the number of simulation scenarios that can be tackled due to the application of the finite-difference scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Yuhao Zhao, Fanhao Guo, Deshui Xu
Summary: This study develops a vibration analysis model of a nonlinear coupling-layered soft-core beam system and finds that nonlinear coupling layers are responsible for the nonlinear phenomena in the system. By using reasonable parameters for the nonlinear coupling layers, vibrations in the resonance regions can be reduced and effective control of the vibration energy of the soft-core beam system can be achieved.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
S. Kumar, H. Roy, A. Mitra, K. Ganguly
Summary: This study investigates the nonlinear dynamic behavior of bidirectional functionally graded plates (BFG) and unidirectional functionally graded plates (UFG). Two different methods, namely the whole domain method and the finite element method, are used to formulate the dynamic problem. The results show that all three plates exhibit hardening type nonlinearity, with the effect of material gradation parameters being more pronounced in simply supported plates.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Isaac A. Garcia, Susanna Maza
Summary: This paper analyzes the role of non-autonomous inverse Jacobi multipliers in the problem of nonexistence, existence, localization, and hyperbolic nature of periodic orbits of planar vector fields. It extends and generalizes previous results that focused only on the autonomous or periodic case, providing novel applications of inverse Jacobi multipliers.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Yongjian Liu, Yasi Lu, Calogero Vetro
Summary: This paper introduces a new double phase elliptic inclusion problem (DPEI) involving a nonlinear and nonhomogeneous partial differential operator. It establishes the existence and extremality results to the elliptic inclusion problem and provides definitions for weak solutions, subsolutions, and supersolutions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Shangshuai Li, Da-jun Zhang
Summary: In this paper, the Cauchy matrix structure of the spin-1 Gross-Pitaevskii equations is investigated. A 2 x 2 matrix nonlinear Schrodinger equation is derived using the Cauchy matrix approach, serving as an unreduced model for the spin-1 BEC system with explicit solutions. Suitable constraints are provided to obtain reductions for the classical and nonlocal spin-1 GP equations and their solutions, including one-soliton solution, two-soliton solution, and double-pole solution.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
