Numerical Analysis and Computation Commons^™

(Si16-04) Some Fixed Point Theorems On Chatterjea Type Contractions, Irom Shashikanta Singh, Y. Mahendra Singh

Applications and Applied Mathematics: An International Journal (AAM)

This paper establishes the existence of fixed points related to strict Chatterjee contractive mappings by relaxing the compactness of the underlying spaces and the continuity of the mapping involved, using altering distance functions and comparison functions in the general setting of metric spaces. Several non-trivial and illustrative examples are provided to demonstrate, support, and validate the obtained theoretical results. In addition, a theorem that can characterize the completeness of metric spaces through the existence of fixed points is rigorously proven and discussed. Furthermore, a theorem on strict Chatterjea-type modulus contractive mappings without continuity assumptions and with relaxed compactness conditions is …

A Coupled Fractional Thermistor System Demonstrating Existence, Uniqueness, And Simulation Results With Two-Point Boundary Conditions, Yahia Awad, Angela Khattar, Hussein Fakih, Sami Hammoud, Karim Amin

Mathematical Modelling and Numerical Simulation with Applications

This paper studies a coupled system of Caputo fractional differential equations of orders $\alpha, \beta\in(1,2]$, subject to two-point boundary conditions. The model incorporates nonlinear nonlocal integral terms that capture the memory-dependent interactions between thermal and electrical dynamics in thermistor materials. We rigorously establish existence via Schaefer’s fixed-point theorem and uniqueness through Banach’s contraction principle in a Banach space of continuous and continuously differentiable functions. Additionally, we analyze Ulam–Hyers stability to quantify solution sensitivity to initial perturbations. A numerical example highlights the effects of fractional orders and nonlocal feedback on system behavior. This work generalizes classical thermistor models and provides a …

The Butterfly Effect In Economics: Exploring Chaos With A Simple Financial Model, Sandy Hs Herho

CODEE Journal

Wild swings in financial markets need not result from external shocks like earthquakes or wars—they can emerge from deterministic chaos. This article introduces kalimusada, an open-source Python library that lets students and instructors explore this phenomenon through a simple three- equation model of financial dynamics. The model couples interest rates, investment, and prices through nonlinear feedback, generating bounded but unpredictable oscillations characteristic of chaos. Tiny differences in starting conditions—smaller than any measurement could detect—grow exponentially until two initially identical economies follow completely different paths. The library provides ready-to-use tools for visualizing this “butterfly effect” in economics, computing divergence metrics, and …

Eigenvalue Bound Preservation: Numerical Experiments On The 2d Q-Tensor Flow, Marcel C. Deguzman

Knowledge and Creativity Expo

We study the evolution of nematic liquid crystals in two dimensions using the Q-tensor model, a continuum framework that describes the orientational order of rod-like molecules via symmetric, traceless matrices. Focusing on the Landau-de Gennes energy and its associated gradient flow, we consider a reduced two-dimensional formulation in which the Q-tensor is fully described by two scalar functions. This reduction simplifies the system to a nonlinear, coupled PDE for the scalars, while preserving essential physical features. A key question is whether the eigenvalues of the Q-tensor remain within the physically admissible range under this flow. Building on a theoretical result …

Computationally Modelling Nmda Blockages Within A Neural Network, Anya Raetsch

UNH URC Open (2026 and after)

The N-Methyl-D-Aspartate (NMDA) Receptor is fundamentally important to memory formation within the brain due to its control of calcium entry into the cell.  In recent years, there has been an increased interest in long-term effects of NMDA blockages on the brain, due to the “re-wiring” of communication channels (synapses) between neurons. This project models the effects of NMDA blockages due to drugs such as Ketamine, and how the blocking of NMDA receptors affects firing rates, which can then be applied to studying long-term plasticity within the neural hierarchies. Using the Nest Online Simulator, a 50x50 grid of neurons was created …

Modeling Landslide-Generated Tsunami For Hazard Analysis: A Case-Study Of Grewingk, Ak, Cassidy J. Deer

All Master's Theses

Landslide-generated tsunamis pose an increasing hazard in glacial and paraglacial environments, where glacial retreat results in slope instability and the potential for mass movement events into a body of water. This thesis analyzes a landslide–generated tsunami at Grewingk Lake in October 1967 by integrating numerical simulations from the D-Claw and GeoClaw models, which are both derived from the Clawpack framework for solving hyperbolic conservation laws. By modeling landslide dynamics and wave propagation in a coupled manner, this study seeks to improve understanding of the hazard, risks and spatial impact at Grewingk. The D-Claw and GeoClaw modeling approaches complement each other …

Using Ai To Analyze Survey Data, Sara Martucci

Open Educational Resources

This assignment in Methodology in Sociology/Criminology engages students in the full research process by guiding them through variable selection, data analysis, interpretation, and critical reflection on AI-assisted decision-making. Using a class-generated survey dataset (or an existing dataset), students develop a research question, identify independent and dependent variables, and formulate a hypothesis. They then compare their selections with those suggested by an AI tool, analyzing differences in reasoning and variable choice. Through SPSS, students generate frequency tables, charts, and scatterplots to examine relationships between variables, including potential intervening factors. The assignment culminates in a group presentation and reflective analysis on the …

Using L1-Magic For Feature Enhancement And Reduced Redundancy In Hyperspectral Data, Ashley Alfred

Mathematics Dissertations

Hyperspectral imaging offers detailed spectral information, but achieving high spatial resolution typically requires large and expensive equipment. This study explores an alternative approach: enhancing low-quality hyperspectral bands using an L1-norm minimization technique known as L1-magic. The goal is to improve the utility of low-cost hardware by preserving discriminative features, promoting sparsity, and reducing spectral redundancy. We apply L1-magic to enhance low-quality bands and hypothesize that this method selectively amplifies key features while suppressing redundant information. Experimental results indicate that the enhanced bands approach the quality of high-resolution data, enabling robust feature extraction without reliance on high-end hyperspectral cameras.

A Bayesian Late-Fusion Supportability Framework For Rare-Disease Severity Prediction In Glut1 Deficiency Syndrome, Jordan M. Rodriguez

Mathematics Dissertations

Glucose transporter type 1 deficiency syndrome (GLUT1-DS) is a rare neurometabolic disorder with heterogeneous neurological and developmental severity. Because patient-level severity is not observed as a single validated outcome, this dissertation develops a Bayesian late-fusion supportability framework for constructing and predicting an ordered latent severity phenotype from clinical, genetic, and EEG-derived evidence. The primary target was constructed in a larger clinical cohort using age-5 symptom burden and learning cognition, then assigned to an aligned multimodal prediction cohort. Target-defining variables were excluded from supervised predictors, and models were evaluated using patient-exclusive cross-validation with training-fold preprocessing and fold-wise EEG PCA.

The primary …

Performance Of Numerical Methods Applied To The Black–Scholes Model, Scott Cameron Williams

UNF Graduate Theses and Dissertations

We compare five numerical approaches for approximating solutions to the Black–Scholes partial differential equation for pricing European call options: FTCS, BTCS, Crank– Nicolson, Monte Carlo simulation, and a physics–informed neural network (PINN). These methods span finite difference techniques, probabilistic simulation, and machine learning. Performance is evaluated based on computational efficiency and accuracy relative to the analytical Black–Scholes solution.

Among the methods, Crank–Nicolson and the PINN demonstrated the strongest overall performance. Crank–Nicolson achieved the highest accuracy but exhibited increased runtime as the number of underlying stock price grid points grew. In contrast, the PINN produced slightly less accurate results but with …

A Mathematical Frameworks For Singular, Nonlinear Phenomena: Applications To Nematocyst Firing And Inhomogeneous Nls With Coulomb Potential, Abdulrahman Alharbi

Theses and Dissertations

Nematocysts are specialized cellular organelles found in all cnidarians, including corals and jellyfish, as well as in some single-celled protists such as dinoflagellates. These organelles display remarkable diversity in morphology and function, playing roles in prey capture and defense. The firing of a nematocyst is one of the fastest accelerations in nature, yet the underlying physical mechanisms remain not fully understood. In this work, we address key questions: how sufficient force is generated to overcome the fluid boundary layer, whether fluid–structure interaction models can reproduce observed dynamics, and what mechanisms trigger discharge.

Our research investigates models based on osmotic pressure …

A Reconstruction Method For The Anisotropic Electrical Conductivity In A Hybrid Planar Inverse Problem, Athanasios Dimitriadis

Graduate Studies Theses and Dissertations 2026

Some single-physics medical imaging methods fail to reliably discriminate benign from malignant biological tissue. In partial response, a new class of inverse problems employ multi-physics phenomena, coupling methods of high resolution with methods of high contrast. In this thesis we are concerned with one such problem in which an anisotropic electrical conductivity is to be recovered from some internal knowledge of the current density field generated by maintaining a fixed boundary voltage. This internal data is obtained by the method of Current Density Impedance Imaging (CDII), which combines Maxwell's equations with Magnetic Resonance Imaging (MRI) measurements. The anisotropy class is …

Microgravity-Induced Alterations In Left Atrial Hemodynamics And Thrombogenic Risk: Insights From Healthy And Atrial Fibrillation Models, Grace M. Hoeppner

Dissertations, Master's Theses and Master's Reports

Background: Microgravity exposure alters cardiovascular loading, yet its impact on left atrial flow dynamics and thrombotic risk remains poorly understood. This study investigates how spaceflight-relevant microgravity-induced changes in cardiac outflow affect left atrial hemodynamics in healthy individuals and patients with atrial fibrillation.

Methods: Patient-specific left atrial models were generated for three healthy individuals and three AF patients. Computational fluid dynamics (CFD) simulations were performed using each patient’s baseline mitral outflow waveform and two modified waveforms representing short- and long-duration post-flight cardiac loading changes derived from echocardiographic observations. Hemodynamic metrics included left atrial velocity, time averaged wall shear stress, oscillatory shear …

(R2151) Error Estimates Of Barycentric Lagrange Interpolation, Alvira Yawar, Swarnima Bahadur

Applications and Applied Mathematics: An International Journal (AAM)

Barycentric interpolation, which comes from Lagrange interpolation, is a useful method in numerical analysis. In this research paper, we explain how the barycentric interpolation formula is derived and discuss its features. We compare its stability and performance with the traditional Lagrange formula. First, we show how to get the barycentric formula from the Lagrange polynomial and present it as a rational function. We also provide an estimate of the error. Then, we use numerical examples to show that the barycentric formula is more stable and works better, especially when the degree of interpolation is high. Our results show that the …

Analysis And Numerical Investigation Of A Breast Cancer Treatment Model Incorporating Ketogenic Diet And Immune Boosters Via Optimal Control Theory, Kunnisai Muniroh, Ummu Habibah, Wuryansari Muharini Kusumawinahyu, Nur’Izzati Hamdan

Mathematical Modelling and Numerical Simulation with Applications

This paper develops a mathematical model to investigate breast cancer dynamics by incorporating tumor–immune interactions, ketogenic diet effects, and medical treatment. The model is formulated as a system of nonlinear ordinary differential equations and analyzed within an optimal control framework. Time-dependent control variables are introduced to represent treatment strategies aimed at minimizing tumor progression while reducing therapeutic costs. The model’s well-posedness is established through positivity and boundedness analysis. The necessary conditions for optimality are derived using Pontryagin’s Minimum Principle, resulting in a coupled system of state and adjoint equations. Numerical solutions are obtained using the fourth-order Runge–Kutta method combined with …

Mathematical Analysis And Numerical Simulation Of A Fractional-Order Sir-Si Model For Malaria Transmission Dynamics, Gassan A. M. O. Farah, Abdulaziz Y. A. Mukhtar, Kailash C. Patidar

Mathematical Modelling and Numerical Simulation with Applications

This study investigates the complex transmission dynamics of malaria, a critical global health challenge, with a focus on the African continent. We introduce a novel approach that employs Fractional Differential Equations (FDEs) to advance the understanding of malaria spread and control. Specifically, we develop a new SIR-SI model using the Caputo fractional operator, which captures the memory effects and time-delay characteristics inherent in real-world epidemiological systems. A detailed analysis of the model's solvability and uniqueness is conducted using fixed-point theory. To obtain an analytical solution, the system is solved via the Laplace transform method, with solutions expressed in closed form …

A Parallel Interval Modeling Framework For Nonlinear Systems: Application To A Modified Duffing Oscillator, Roman Voliansky, Nina Volianska

Northeast Journal of Complex Systems (NEJCS)

The paper presents a mathematical framework for converting nonlinear dynamical systems into parallel forms. This framework replaces the exact system motion equations with interval equations, enabling the representation of nonlinear functions over piecewise linear domains. Such representation enables the description of system motions using linear-like differential equations, which can be analyzed and manipulated using well-known control methods. One such method is eigenvalue analysis, a powerful tool in classical control theory since many techniques rely on the system’s characteristic polynomial and its eigenvalues. We apply this method to define interval system eigenvalues and track their variation during system operation. These eigenvalues …

(R2134) Continuous Shooting Approach With Improved Shooting Slope For Solving Higher Integer Order Boundary Value Problem, Razaq Adekola Oderinu, Adebowale Niyi Aderibigbe, Saheed Alao, Ahmed Adeyi Yahaya

Applications and Applied Mathematics: An International Journal (AAM)

This study presents a semi-analytical shooting method for solving nonlinear higher-order boundary value problems by integrating the Adomian Decomposition Method into the shooting technique, enabling series-form solutions. To enhance convergence, new higher-order shooting slopes and their corresponding supplementary equation formulas were introduced. Three numerical examples demonstrated the method’s accuracy: for the first two, absolute errors were computed using available exact solutions, while the third was compared with reference literature due to the absence of an exact solution. The method achieved very small absolute errors in the first two cases, and results from the third closely matched the literature. Tolerance values—defined …

Coupled Machine Learning Models: Combining Observations And Numerical Analysis In A Physics-Regularized Approach, Austin B. Schmidt

LSU New Orleans Theses and Dissertations

This dissertation investigates surrogate modeling for fixed-location environmental forecasting using novel data-combination techniques. The work surveys the landscape of observational measurements and numerically generated data, identifying similar research and gaps in current methodologies. The ratio-coupled training framework is introduced to combine two data sources per predicted feature through a tunable parameter that weights training signal strength. An optimization scheme is developed to simultaneously tune surrogate weights and the coupled signal ratio, allowing relative influence between signals to act as an explicit regularizer. Three case studies demonstrate the methodology and approach in a variety of contexts. The first study is based …

(R2135) System Dynamical Analysis For Ann-Based Numerical Solutions Of A Compartmental Model: A Bio-Mathematical Model Of Drug Diffusion Through The Compartments Of Blood And Tissue, Rakesh Kumar, Sudarshan Dhua

Applications and Applied Mathematics: An International Journal (AAM)

This paper provides a considerably efficient numerical approach to acquire the solutions of a biomathematical model administrating oral and intravenous distribution of pharmaceuticals in the human body. The proposed numerical approach based on an artificial neural network is employed to extract numerical solutions for a detailed set of ordinary differential equations and analyze the change in concentration of drug diffusion via the compartments of blood and tissue medium. We primarily focus on analyzing three different models established on the diffusion process, exercising laws of mass action and Fick’s principle. In this work, the existing model is reformulated as an optimization …