Transforming frontiers: The next decade of differential equations and control processes

Advances in Differential Equations and Control Processes, Год журнала: 2025, Номер 32(1), С. 2589 - 2589

Опубликована: Янв. 22, 2025

Mathematics serves as the fundamental basis for innovation, propelling technological advancement. In forthcoming decade, convergence of differential equations and control processes is poised to redefine frontiers scientific exploration. The integration artificial intelligence machine learning with set inaugurate a new era problem-solving, enabling extraction latent physical insights accelerating solution discovery. Multi-scale modeling, its capacity span disparate domains, has potential resolve long-standing puzzles in fields such fluid mechanics nanoscience. Furthermore, fractal geometry holds promise novel perspectives understanding optimizing complex systems, ranging from urban landscapes turbulent flows. (AI) innovations play pivotal role development next-generation technologies, transform diverse sectors medicine, communication, autonomous systems. This paper explores these developments, highlighting their impacts emphasizing necessity interdisciplinary collaboration leverage full potential.

Язык: Английский

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Nonlinear Coupled Equations Free-Boundary Problem in Atherosclerosis: Symmetry Analysis of Solutions and Numerical Simulation

Symmetry, Год журнала: 2025, Номер 17(2), С. 244 - 244

Опубликована: Фев. 6, 2025

Atherosclerosis, a chronic inflammatory cardiovascular disease closely related to plaque formation during arteriosclerosis, poses significant threat global health. To deepen the understanding of multifaceted interactions driving atherosclerosis progression and provide theoretical support for designing targeted therapeutic strategies, this study establishes nonlinear coupled atherosclerotic free-boundary model integrating immune cells, cytokines, oxidized low-density lipoprotein. By applying compression mapping principle, local existence uniqueness solutions are proven, while revealing certain symmetries in model’s solution structure. Under specific assumptions, quasi-steady-state approximate is derived, its demonstrated. Through numerical simulations using finite difference method, temporal spatial evolution pro-inflammatory macrophages lipoprotein analyzed. The findings highlight strength capturing intricate dynamics atherosclerosis, uncovering underlying mechanisms identifying targets. evaluating across types stenosis levels, experimental design further validated ability replicate clinical processes reinforced predictive accuracy. Notably, process analysis solution, equations boundary conditions play crucial role determining properties. However, current one-dimensional has limitations. Future research should focus on developing higher-dimensional models more influencing factors enhance applicability complex disease.

Язык: Английский

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An efficient space–time two-grid difference approach to symmetric regularized long waves: Enhanced efficiency and accuracy

Alexandria Engineering Journal, Год журнала: 2025, Номер 121, С. 53 - 65

Опубликована: Фев. 25, 2025

Язык: Английский

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Modified Lagrange Interpolating Polynomial (MLIP) Method: A Straightforward Procedure to Improve Function Approximation

AppliedMath, Год журнала: 2025, Номер 5(2), С. 34 - 34

Опубликована: Март 27, 2025

This work presents the modified Lagrange interpolating polynomial (MLIP) method, which aims to provide a straightforward procedure for deriving accurate analytical approximations of given function. The method introduces an exponential function with several parameters multiplies one terms polynomial. These will adjust their values ensure that proposed approximation passes through points target function, while also adopting correct its derivative at points, showing versatility. polynomials (LIPs) present problem introducing oscillatory and are, therefore, expected poor We see relevant contributions MLIPs is contain fewer compared those obtained by LIPs when both pass same be represented; consequently, better MLIP are expected. A comparison results from other methods reported in literature highlights method’s potential as useful tool obtaining set points. It this contributes break paradigm effective modification known has lengthy complex.

Язык: Английский

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Mathematical approach for rapid determination of pull-in displacement in MEMS devices

Frontiers in Physics, Год журнала: 2025, Номер 13

Опубликована: Апрель 7, 2025

Introduction Microelectromechanical systems (MEMS) are pivotal in diverse fields such as telecommunications, healthcare, and aerospace. A critical challenge MEMS devices is accurately determining the pull-in displacement voltage, which significantly impacts device performance. Existing methods, including variational iteration method homotopy perturbation method, often fall short providing precise estimations of these parameters. Methods This study introduces a novel mathematical approach that combines physical insights into phenomenon with theory. The begins definition device's model. By uniquely applying principle incorporating custom-designed functional, set equations derived. These transformed an iterative algorithm for calculating displacement, nonlinear terms addressed through approximation techniques tailored to system’s characteristics. Results Validation using specific examples demonstrates method's accuracy voltage. For instance, oscillator case, exact results were achieved computation time 0.015 s. Compared traditional this yields values rather than approximations, showcasing superior precision efficiency. Discussion proposed offers significant advantages, enhanced accuracy, reduced computational time, minimized error accumulation by solving algebraic instead iterating differential equations. It also exhibits robustness variations initial conditions system Limitations include need modifying criterion when formulation unattainable exclusion environmental factors like temperature pressure fluctuations. Future research should focus on refining models incorporate integrating Galerkin technology. Conclusion advances understanding behavior holds substantial potential design optimization across various applications, further driving progression

Язык: Английский

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Deep learning-based Adam optimization for magnetohydrodynamics radiative thin film flow of ternary hybrid nanofluid with oscillatory boundary conditions

Chaos Solitons & Fractals, Год журнала: 2025, Номер 196, С. 116448 - 116448

Опубликована: Апрель 19, 2025

Язык: Английский

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