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7 articles for “weakly nonlinear equations”
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Compare Newton-HSS Iteration Method and Picard-HSS Iteration Method for Solving the System of Weakly Nonlinear Equations
Abstract: So far several iterative methods have been proposed and used for solving the system of weakly nonlinear equations Ax = G(x). In this paper, we study the Newton-HSS iteration method and Picard-HSS iteration method for solve the system of weakly nonlinear equations. Then we compare these two methods. We discuss the performance of these methods, and numerical results. Cite this ArticleElham Farazande Shahraki. Compare Newton-HSS iteration method and Picard-HSS iteration …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 3, Issue 1, 2016 · pp. 1–6 Read article
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Advance Fixed Point Theorems and Its Application to Ordinary and Fractional Differential Equations
Abstract: In the present research, advanced results on the fixed point theorem are applied to typical boundary value problems. Finding a differential equation's solution under certain boundary conditions is the goal of typical boundary value topics. The article appears to extend new fixed point results to a new context, likely involving fractional operators with unique kernels, notably the Caputo-type fractional operator. This extension involves applying the fixed point theorem to a …
Published in Recent Trends in Mathematics · Vol. 1, Issue 1, 2024 · pp. 1–15 Read article
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Mathematical Modeling of Tumor Growth and Immune System Interaction Incorporating Time Delays and Suppression Effects for Tumor Control
Abstract: Cancer growth is a complex biological process influenced by various factors, including the dynamic interaction between tumor cells and the host immune system. Mathematical modeling serves as a powerful tool to understand these interactions and predict the outcomes of different therapeutic strategies. This study presents a mathematical framework that captures the essential dynamics of tumor-immune interactions, specifically incorporating the effects of time delay and immune suppression mechanisms. Time delay accounts …
Published in Research and Reviews : A Journal of Immunology · Vol. 15, Issue 3, 2025 · pp. 25–34 Read article
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Study of Heat Transfer in a Time Dependent Vertically Oscillating Micropolar Liquid
Abstract: AbstractThe study involves the vertical time periodic vibration of the system. This leads to the appearance of a modified gravity term in basic equation, collinear with actual gravity, in the form of a time-periodic field perturbation and is termed as gravity modulation or g-jitter in the literature. The aim of this study is to find the effect of small amplitude of gravity modulation on the onset of thermal convection between …
Published in Recent Trends in Fluid Mechanics · Vol. 5, Issue 1, 2018 · pp. 63–74 Read article
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Mathematical Approaches to Nonlinear Oscillatory Systems with Damping: Exact and Approximate Solutions
Abstract: The study of nonlinear oscillatory systems with damping is a key area of research in applied mathematics, particularly in the context of dynamical systems, stability analysis, and bifurcation theory. These systems, described by second-order nonlinear differential equations, exhibit a rich variety of behaviors, including periodic, quasi-periodic, and chaotic motions. The introduction of damping—representing energy dissipation—adds a layer of complexity, making the analytical and numerical solution of such systems a challenging …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 7–11 Read article
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Numerical Investigation of Slip Conditions in Nanofluid Flow Induced by a Nonlinearly Stretching Sheet: A bvp4c Approach
Abstract: The present work describes a numerical analysis of the steady, laminar flow over a nonlinear stretching sheet in a nanofluid medium. Slip conditions in terms of velocity, temperature, and concentration have been introduced into the mathematical model to capture the impact of interfacial mass transfer on the stretching surface. The problem is modeled to include nanoparticle transportation in terms of Brownian diffusion and thermophoresis, thereby affecting the temperature and concentration …
Published in Recent Trends in Fluid Mechanics · Vol. 13, Issue 2, 2026 · pp. 34–51 Read article
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Extended Fixed Point Theorems in Menger PM-Type Spaces: Generalized Auxiliary Functions and Contractivity Conditions
Abstract: Background: Fixed point theory in probabilistic metric spaces, particularly Menger spaces, has been a subject of intensive research due to its applications in nonlinear analysis and mathematical modeling. Traditional approaches often impose restrictive constraints on the defining properties of Menger spaces and limit the class of auxiliary functions in contractivity conditions Methods: We extend recent fixed point theorems in Menger spaces by: (1) introducing the notion of Menger PM-type spaces …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 3, 2025 · pp. 1–6 Read article