Numerical Analysis and Computation Commons^™

(R2100) Optimality Conditions Of A Topsis Optimization Model And Its Application On Interval-Valued Data, Sudipta Roy, Sandip Chatterjee

Applications and Applied Mathematics: An International Journal (AAM)

The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is widely used in the field of multi-criteria decision analysis. Despite its popularity and widespread application, little attention has been given to the mathematical foundation that underlies the TOPSIS algorithm. The existing literature on this subject is far from comprehensive, leaving many aspects of the algorithm unexplored. This paper aims to address this gap in the literature by delving into the optimization problem associated with TOPSIS. Unlike traditional interval analysis theory, which only covers a limited scope, our approach extends to a broader range of scenarios and offers …

(R2113) A Numerical Method For Solving Linear First-Order Volterra Integro-Differential Equations With Integral Boundary Condition, Zelal Temel, Musa Cakir

Applications and Applied Mathematics: An International Journal (AAM)

We investigate an efficient numerical method for the linear first-order Volterra integro-differential equations with integral boundary condition. To solve this problem, boundaries are determined for its derivative and the solution. The numerical solutions of the problem are modeled over a uniform mesh using the composite right-side rectangle concept for the integral component and the implicit difference rules for the differential component. Next, the stability and convergence of the numerical approach are discussed. The numerical experiments are presented confirming the accuracy of the proposed scheme.

Question-Attentive Review-Level Explanation For Neural Rating Regression, Trung Hoang Le, Hady Wirawan Lauw

Research Collection School Of Computing and Information Systems

Recommendation explanations help to improve their acceptance by end users. Explanations come in many different forms. One that is of interest here is presenting an existing review of the recommended item as the explanation. The challenge is in selecting a suitable review, which is customarily addressed by assessing the relative importance or “attention” of each review to the recommendation objective. Our focus is improving review-level explanation by leveraging additional information in the form of questions and answers (QA). The proposed framework employs QA in an attention mechanism that aligns reviews to various QAs of an item and assesses their contribution …

Modelling Saccharomyces Cerevisiae For The Production Of Fermented Beverages, Paul A. Valle Dr., Yolocuauhtli Salazar Dr., Luis N. Coria Dr., Oscar N. Soto Dr., Jesus B. Paez Dr.

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Bayesian Networks And Machine Learning For Predicting Breast Cancer Growth From In Vitro Cell Count Data, Widodo Samyono

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Seshaiyer: Understanding Non-Linear Dynamics Of Interacting Subpopulations And Implicit Human Behavior Using Physics-Informed Neural Networks, Naima Aubry-Romero, Alonso Ogueda-Oliva, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

An Introduction To The Time-Independent Schrödinger Equation And Methods To Solve It, Vu Giang, Alex Gnech

OUR Journal: ODU Undergraduate Research Journal

The Time-Independent Schrödinger Equation is a linear elliptic PDE that describes quantum-mechanical systems. Its significance in the science of submicroscopic phenomena, particularly quantum mechanics, is as central as Newton’s laws of motion are to classical mechanics. This study uses various methods, including novel neural networks and finite difference schemes, to solve the one-dimensional two-body equation.

(Si13-09) Numerical Methods For Solving Nonlinear Fisher Equation Using Backward Differentiation Formula, Vikash Vimal, Rajesh Kumar Sinha, Liju Pannikkal

Applications and Applied Mathematics: An International Journal (AAM)

This paper examines the numerical solution of the nonlinear Fisher equation that is used to find the growth of tumour cells in the brain. By employing new methods that transform nonlinear partial differential equations (PDE) into nonlinear ordinary differential equations (ODE) through spatial discretization. The stability of the resulting nonlinear system is evaluated using Lyapunov’s criteria. Implicit stiff solvers, including various orders of backward differentiation formulas, are used to address the ODE system. The efficiency of these numerical methods is demonstrated through two examples, and a comparison with existing methods from the literature is conducted. Compared to traditional methods, the …

(Si13-02) Approximate Solution Of Fuzzy Volterra Integro-Differential Equations Using Numerical Techniques, Asiya Ansari, Najmuddin Ahmad

Applications and Applied Mathematics: An International Journal (AAM)

To determine the approximate solution to fuzzy Volterra integro-differential equations, the Adomian Decomposition Method (ADM), Modified Adomian Decomposition Method (MADM), Variational Iteration Method (VIM), and Homotopy Perturbation Method (HPM) are proposed in this study. We present two examples to support the methodology, and the results are presented in tables to demonstrate the method’s efficiency and correctness. Wolfram Mathematica 11.3 is used to perform the computations.

Production Box Cost Estimating Relationships For Dod Avionics, Carla J. Cisneros, Edward D. White, Brandon M. Lucas, Jonathan D. Ritschel, Robert D. Fass, Shawn M. Valentine

Faculty Publications

The authors use historical information obtained from the Cost Assessment Data Enterprise to estimate recurring production unit cost for DoD avionics via cost estimating relationships (CERs). The specific modeled responses include mean unit cost, median unit cost, and the 100th production unit cost (T100) utilizing learning curve theory. For T100, the authors adopt both a multiplicative and an additive error for CER comparison. Recommended CERs consist of the mean unit cost and the T100 utilizing a multiplicative error. Moreover, results reveal that weight has a significant effect on cost as well as a potential underaccounting of real price change or …

Performance Studies Of An Axial Flow Waterjet Pump Using An Unsteady Reynolds-Averaged Navier-Stokes Model, Stephen E. Monroe, Junfeng Wang, Chunlei Liang

Northeast Journal of Complex Systems (NEJCS)

In this study, an Unsteady Reynolds-Averaged Navier-Stokes (URANS) model is demonstrated its suitability for studying the flow and performance of open marine propellers and waterjet pumps. First, the accuracy of the URANS model is validated by studying turbulent flow past counter-rotating propellers (CRPs). Specifically, experimental data from Miller (1976) is employed for comparison against the URANS results. Subsequently, URANS is used to study the flow and performance of an Office of Naval Research (ONR) axial flow waterjet pump (AxWJ-2). Due to the large number of degrees of freedom for both simulations, parallel computations over 80 cores are performed. For the …

Certifying Stability In Runge-Kutta Schemes: Algebraic Conditions And Semidefinite Programming, Austin Juhl

Dissertations

Numerical stability is a critical property for a time-integration scheme. In the context of Runge-Kutta methods applied to stiff differential equations, A-stability is one of the most basic and practically important notions of stability. Dating back to the work of Dahlquist, it has been known that A-stability is equivalent to the Runge-Kutta stability function satisfying a particular convex feasibility problem. Specifically, up to a transformation, the stability function lies in the convex cone of positive functions. In recent years, sum-of-squares optimization and semidefinite programming have become valuable tools in developing rigorous certificates of stability in dynamical systems. Therefore, it is …

Exploring The Transformation Of Sustainable Collective Spaces: A Study From Mlalakuwa Informal Settlement, Jacob Lutta

Tanzania Journal of Engineering and Technology (TJET)

A major challenge in collective space transformation is addressing the complexity of informal urbanisation in developing countries. Using a case study approach, this paper examines the concerns related to a particular informal settlement's sustainable collective space transformation. One of the key findings is that the absence of formal rules and regulations in the development of informal settlements in combination with land-grabbing leads to the absence of open spaces that could be used collectively. It is observed that sustainability in urban development is another body of critical thought that integrates several streams of current urban elements and embodies various conceptions of …

Evaluation Of Business-Driven Reference Architecture For Big Data Analytics Implementation By Public Sector Organizations In Resource-Constrained Setting: A Case Study Of Uganda, Matendo Didas

Tanzania Journal of Engineering and Technology (TJET)

Big Data Analytics (BDA) is a new area at the nexus of agenda, public sector organizations, and government business. It may satisfy the growing need for trustworthy, cost-effective services in the public sector for better, more informed decision-making processes. BDA has been proposed on the planning schedules of several public sector organizations and the government. Therefore, from the previous work, using Uganda as a case study, specifically the Uganda Bureau of Statistics (UBOS), Ministry of Health (MoH), and Ministry of Education and Sports (MoES), this study aims to evaluate a designed Business-Driven Reference Architecture for Big Data Analytics Implementation (BRABDAI) …

Investigation Of Heavy Metal Composition And Associated Health Risks From Selected Groundwater Wells In Temeke, Dar-Es-Salaam, Justin M. Jeremiah

Tanzania Journal of Engineering and Technology (TJET)

Water quality continues to be the challenge to residents in Dar es Salaam due to various anthropogenic activities in the city. This study was conducted to assess groundwater quality by determining concentrations of heavy metals. Both probability and Nonprobability sampling techniques were used to collect samples from 40 groundwater wells in 24 wards of Temeke municipal and analysed using Microwave Plasma Atomic Emission Spectrometer (Agilent 4210 MP-AES) at the Geochemistry Laboratory of the University of Dar es Salaam. Results indicated varying heavy metal concentrations ranging from 0.71 ± 0.08 to 6.64 ± 0.21 mg/l for As, 0.02 ± 0.01 to …

Perona-Malik Diffusion-Driven Regularization For Image Resolution Enhancement In Electrical Capacitance Tomography, Nassor Ally

Tanzania Journal of Engineering and Technology (TJET)

Electrical Capacitance Tomography (ECT) is a non-invasive promising method for monitoring industrial processes, such as oil-gas flow in pipelines and solid-gas flow in pneumatic systems. Despite its potential benefits, ECT generates poor-quality images, often used only for qualitative analysis. A non-linear relationship between measured capacitances and permittivity distribution and the ill-posedness of the sensitivity matrix elements causes this limitation. This hinders the applicability of ECT in monitoring online industrial process applications. This work proposes a reconstruction method based on a nonlinear diffusion function to generate high-quality images from the measured capacitance data from the ECT system. The diffusion regularization functional …

Assessing The Importance Of Air-Decking Blasting In Controlling Bigv At An Open Pit Gold Mine In Tanzania Using Ann Model, Karim R. Baruti

Tanzania Journal of Engineering and Technology (TJET)

Air-decking blasting technique is used to control blast induced ground vibration (BIGV) in several mines including open-pit gold mines located in Tanzania. While the importance of air-deck to control BIGV is practically evident, theoretical models such as BIGV prediction models cannot be used to assess the importance of air-decking. The main objective of this study was to assess the importance of the air-decking blasting technique to control BIGV using the artificial neural network (ANN)Model. To achieve this objective, ANNs were modeled and trained to learn the pattern of data using Multilayer Perception with Back Propagation to predict BIGV. The main …

Mathematical Modeling, Analysis, And Simulation Of Patient Addiction Journey, Adan Baca, Diego Gonzalez, Alonso G. Ogueda, Holly C. Matto, Padmanabhan Seshaiyer

CODEE Journal

This paper aims to develop a mathematical model to study the dynamics of addiction as individuals go through their detox journey. The motivation for this work is three fold. First, there has been a significant increase in drug overdose and drug addiction following the COVID-19 pandemic, and addiction may be interpreted as a infectious disease. Secondly, the dynamics of infectious disease could be modeled via compartmental models described by differential equations and one can therefore leverage the existing analytical and numerical methods to model addiction as a disease. Finally, the work helps to inform how mathematical models governed by differential …

Hypogene Speleogenesis In Carbonates By Cooling Hydrothermal Flow: The Case Of Mt. Berenike Caves, Israel, Roi Roded, Boaz Langford, Einat Aharonov, Piotr Szymczak, Micka Ullman, Shemesh Yaaran, Boaz Lazar, Amos Frumkin

International Journal of Speleology

The Berenike hypogenic cave system near Lake Kinneret, Israel, provides a valuable case study for investigating the recently proposed Confined-Cooling-Flow (CCF) speleogenesis model. Field and speleological surveys, along with existing research, are used to provide a thorough analysis. The CCF model relies on a simple thermo-hydro-chemical scenario, involving the rise of CO2-rich hydrothermal fluids discharging into a confined layer. The cooling of these CO2-rich fluids turns them into aggressive solutions due to the inverse relation between temperature and solubility of carbonates (retrograde solubility). Previous geochemical and numerical analyses of the CCF model predict localized and persistent dissolution and speleogenesis on …

Delta-Shaped Approximation Based Homotopy Analysis Method For Nonlinear Poisson-Type Partial Differential Equations, Cyril Ocloo

Dissertations

This research aims to solve nonlinear Poisson-type partial differential equations (PDEs) by the approach of the homotopy analysis method (HAM) incorporated with approximate particular solutions (APS) using Delta-shaped basis (DSB) approximations.

With the inclusion of the h auxiliary parameters, we tackle nonlinear problems by studying the mathematical characteristics of the h curve. This is to ensure the numerical convergence of the HAM.

In the solution process, we use the homotopy analysis method to convert a nonlinear PDE into linear inhomogeneous PDEs, which are solved using the method of approximate particular solutions with DSB.

A proper value of the h is …

Computation Of Moving Interface Flows In Biophysical Applications, Mohammad Murshed

Masters Theses and Doctoral Dissertations

This dissertation is concerned with the modeling, simulation, and analysis of moving interface problems involving viscous fluids and solid structures. The main computational technique employed in this work is the immersed boundary method, a widely known numerical method for fluid-structure interaction (FSI). In this technique, the fluid equations are solved in an Eulerian grid and the structure is treated as a network of Lagrangian nodes. The communication between the fluid and structure dynamics is established by the use of the Dirac delta function. Utilizing the immersed boundary method, we have studied three biophysical applications. In the first application, we computed …

Scalable Solution Of Time-Dependent Pdes Through Component-Wise Exponential Integrator, Chelsea Drum

Dissertations

Exponential integrators, such as exponential Runge-Kutta or Rosenbrock methods, are designed specifically for the time integration of stiff systems of ordinary differential equations (ODEs) and allow the use of larger time steps than other general-purpose ODE solvers. However, these methods rely on computing matrix function-vector products that are traditionally computed using a Krylov projection, such as Lanczos or Arnoldi iteration, that involves substantial computational expense at high spatial resolution. Krylov Subspace Spectral (KSS) methods' frequency-dependent approach, designed to circumvent stiffness in linear problems, computes these products with greater scalability. We propose the combination of such KSS methods with exponential integrators …

Uniformly Distributing Points On A Sphere, Flavio Arrigoni

Rose-Hulman Undergraduate Mathematics Journal

In this paper, we are going to present and discuss different procedures for distributing points on a sphere's surface. Furthermore, we will assess their quality with three different distribution tests. The MATHEMATICA package that we created for testing and plotting the points is publicly available.

Approximating Equilibria In Restricted Games, Jack W. Doyle

Rose-Hulman Undergraduate Mathematics Journal

We consider optimal play in restricted games with linear constraints, and use ϵ-equilibria to find near-equilibrium states in these games. We present three mathematical optimization formulations -- a mixed-integer linear program (MILP), a quadratic program with linear constraints (QP), and a quadratically constrained program (QCP) -- to both approximate and identify these states. The MILP has a short runtime relative to the QP and QCP for large games (a factor 100 faster for |S|=9) and exhibits linear growth in run time, but provides only relatively weak upper bound. The QP and QCP provide a tight bound and the precise value …

Numerical Issues For A Non-Autonomous Logistic Model, Marina Mancuso, Kaitlyn M. Martinez, Carrie Manore, Fabio Milner

CODEE Journal

The user-friendly aspects of standardized, built-in numerical solvers in
computational software aid in the simulations of many problems solved using
differential equations. The tendency to trust output from built-in numerical
solvers may stem from their ease-of-use or the user’s unfamiliarity with the
inner workings of the numerical methods. Here, we show a case where the
most frequently used and trusted built-in numerical methods in Python’s
SciPy library produce incorrect, inconsistent, and even unstable approxima-
tions for a the non-autonomous logistic equation, which is used to model
biological phenomena across a variety of disciplines. Some of the most com-
monly used …

(R2067) Solutions Of Hyperbolic System Of Time Fractional Partial Differential Equations For Heat Propagation, Sagar Sankeshwari, Vinayak Kulkarni

Applications and Applied Mathematics: An International Journal (AAM)

Hyperbolic linear theory of heat propagation has been established in the framework of a Caputo time fractional order derivative. The solution of a system of integer and fractional order initial value problems is achieved by employing the Adomian decomposition approach. The obtained solution is in convergent infinite series form, demonstrating the method’s strengths in solving fractional differential equations. Moreover, the double Laplace transform method is employed to acquire the solution of a system of integer and fractional order boundary conditions in the Laplace domain. An inversion of double Laplace transforms has been achieved numerically by employing the Xiao algorithm in …

(R2078) Analyzing The Effects Of Fifth And Seventh Order Terms In A Generalized Henon-Heiles Potential, Nandana Madhukara

Applications and Applied Mathematics: An International Journal (AAM)

The Hénon-Heiles system is a 2-dimensional axisymmetric Hamiltonian system that was first formed to determine the third integral of motion in galactic dynamics. After its inception, it has become a paradigm in dynamical systems due to its apparent simplicity but extremely complicated dynamical behavior. In this paper, we perform a series expansion up to the seventh order of a general potential with axial and reflection symmetries. After some transformations, this becomes a generalized Hénon-Heiles (GHH) system where we separate the fifth and seventh-order terms. We qualitatively analyze this system for energies near the threshold between bounded and unbounded motion with …

Pt-Symmetry And Eigenmodes, Tamara Gratcheva

University Honors Theses

Spectra of systems with balanced gain and loss, described by Hamiltonians with parity and time-reversal (PT) symmetry is a rich area of research. This work studies by means of numerical techniques, how eigenvalues and eigenfunctions of a Schrodinger operator change as a gain-loss parameter changes. Two cases on a disk with zero boundary conditions are considered. In the first case, within the enclosing disk, we place a parity (P) symmetric configuration of three smaller disks containing gain and loss media, which does not have PT-symmetry. In the second case, we study a PT-symmetric configuration …

Advances In Computational And Statistical Inverse Problems, Dylan Green

Dartmouth College Ph.D Dissertations

Inverse problems are prevalent in many fields of science and engineering, such as signal processing and medical imaging. In such problems, indirect data are used to recover information regarding some unknown parameters of interest. When these problems fail to be well-posed, the original problems must be modified to include additional constraints or optimization terms, giving rise to so-called regularization techniques. Classical methods for solving inverse problems are often deterministic and focus on finding point estimates for the unknowns. Some newer methods approach the solving of inverse problems by instead casting them in a statistical framework, allowing for novel point estimate …

Identifiability For Pde Models Of Fluorescence Microscopy Experiments, Veronica Ciocanel

Biology and Medicine Through Mathematics Conference

No abstract provided.