arXiv subjects

Md. Shafiqul Islam

Publications and source records attributed to Md. Shafiqul Islam.

11 recordsLinked to original sources

arXiv2026

Artificial Intelligence Literacy and Sustainable Development: An Ethical Governance and Development Goals Framework

AI literacy provides foundational competencies that support ethical, transparent, and sustainable technological development, although higher-order capabilities such as governance, critical evaluation, and strategic decision-making extend beyond basic literacy into advanced levels of AI competency. This study positions AI literacy as a governance capacity that complements and strengthens all 17 SDGs. It introduces a six-level taxonomy of artificial intelligence reasoning and ethics that extends traditional learning models by incorporating ethical judgement and strategic foresight. This taxonomy forms the foundation of an integrated framework linking education, governance, and sustainable development. A survey of 300 participants from diverse professional backgrounds within a national context which reveals strong technical awareness but limited ethical and governance readiness, highlighting critical gaps in public capacity to manage artificial intelligence responsibly. Findings show that ethical reasoning and reflective thinking are the strongest predictors of sustainable and trustworthy artificial intelligence use. The study proposed to embed literacy-based competencies into curricula, institutional policies, and governance mechanisms to accelerate equitable and responsible progress toward sustainable development goals

cs.CV↗

arXiv2025

PC-DeepNet: A GNSS Positioning Error Minimization Framework Using Permutation-Invariant Deep Neural Network

Global navigation satellite systems (GNSS) face significant challenges in urban and sub-urban areas due to non-line-of-sight (NLOS) propagation, multipath effects, and low received power levels, resulting in highly non-linear and non-Gaussian measurement error distributions. In light of this, conventional model-based positioning approaches, which rely on Gaussian error approximations, struggle to achieve precise localization under these conditions. To overcome these challenges, we put forth a novel learning-based framework, PC-DeepNet, that employs a permutation-invariant (PI) deep neural network (DNN) to estimate position corrections (PC). This approach is designed to ensure robustness against changes in the number and/or order of visible satellite measurements, a common issue in GNSS systems, while leveraging NLOS and multipath indicators as features to enhance positioning accuracy in challenging urban and sub-urban environments. To validate the performance of the proposed framework, we compare the positioning error with state-of-the-art model-based and learning-based positioning methods using two publicly available datasets. The results confirm that proposed PC-DeepNet achieves superior accuracy than existing model-based and learning-based methods while exhibiting lower computational complexity compared to previous learning-based approaches.

cs.LG↗

arXiv2024

A Double-Difference Doppler Shift-Based Positioning Framework with Ephemeris Error Correction of LEO Satellites

In signals of opportunity (SOPs)-based positioning utilizing low Earth orbit (LEO) satellites, ephemeris data derived from two-line element files can introduce increasing error over time. To handle the erroneous measurement, an additional base receiver with a known position is often used to compensate for the effect of ephemeris error when positioning the user terminal (UT). However, this approach is insufficient for the long baseline (the distance between the base receiver and UT) as it fails to adequately correct Doppler shift measurement errors caused by ephemeris inaccuracies, resulting in degraded positioning performance. Moreover, the lack of clock synchronization between the base receiver and UT exacerbates erroneous Doppler shift measurements. To address these challenges, we put forth a robust double-difference Doppler shift-based positioning framework, coined 3DPose, to handle the clock synchronization issue between the base receiver and UT, and positioning degradation due to the long baseline. The proposed 3DPose framework leverages double-difference Doppler shift measurements to eliminate the clock synchronization issue and incorporates a novel ephemeris error correction algorithm to enhance UT positioning accuracy in case of the long baseline. The algorithm specifically characterizes and corrects the Doppler shift measurement errors arising from erroneous ephemeris data, focusing on satellite position errors in the tangential direction. To validate the effectiveness of the proposed framework, we conduct comparative analyses across three different scenarios, contrasting its performance with the existing differential Doppler positioning method. The results demonstrate that the proposed 3DPose framework achieves an average reduction of 90% in 3-dimensional positioning errors compared to the existing differential Doppler approach.

cs.IT↗

arXiv2024

Galerkin-Bernstein Approximations for the System of Third-Order Nonlinear Boundary Value Problems

This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in details, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory.

math.NA↗

arXiv2024

Approximation of Some Nonlinear Fractional Order BVPs by Weighted Residual Methods

To extract the approximate solutions in the case of nonlinear fractional order differential equations with the homogeneous and nonhomogeneous boundary conditions, the weighted residual method is embedded here. We exploit three methods such as Galerkin, Least Square, and Collocation for the efficient numerical solution of nonlinear two-point boundary value problems. Some nonlinear cases are examined for observing the maximum absolute errors by the considered methods, demonstrating the accuracy and reliability of the present technique using the modified Legendre and modified Bernoulli polynomials as weight functions. The mathematical formulations and computational algorithms are more straightforward and uncomplicated to understand. Absolute errors and the graphical representation reflect that our method is more accurate and reliable.

math.NA↗

arXiv2023

Galerkin-Bernstein Approximations of the System of Time Dependent Nonlinear Parabolic PDEs

The purpose of the research is to find the numerical solutions to the system of time dependent nonlinear parabolic partial differential equations (PDEs) utilizing the Modified Galerkin Weighted Residual Method (MGWRM) with the help of modified Bernstein polynomials. An approximate solution of the system has been assumed in accordance with the modified Bernstein polynomials. Thereafter, the modified Galerkin method has been applied to the system of nonlinear parabolic PDEs and has transformed the model into a time dependent ordinary differential equations system. Then the system has been converted into the recurrence equations by employing backward difference approximation. However, the iterative calculation is performed by using the Picard Iterative method. A few renowned problems are then solved to test the applicability and efficiency of our proposed scheme. The numerical solutions at different time levels are then displayed numerically in tabular form and graphically by figures. The comparative study is presented along with L2 norm, and L infinity norm.

math.NA↗

arXiv2023

Numerical Approximations of a Class of Nonlinear Second-Order Boundary Value Problems using Galerkin-Compact Finite Difference Method

In this study, we examine numerical approximations for 2nd-order linear-nonlinear differential equations with diverse boundary conditions, followed by the residual corrections of the first approximations. We first obtain numerical results using the Galerkin weighted residual approach with Bernstein polynomials. The generation of residuals is brought on by the fact that our first approximation is computed using numerical methods. To minimize these residuals, we use the compact finite difference scheme of 4th-order convergence to solve the error differential equations in accordance with the error boundary conditions. We also introduce the formulation of the compact finite difference method of fourth-order convergence for the nonlinear BVPs. The improved approximations are produced by adding the error values derived from the approximations of the error differential equation to the weighted residual values. Numerical results are compared to the exact solutions and to the solutions available in the published literature to validate the proposed scheme, and high accuracy is achieved in all cases

math.NA↗

arXiv2023

Approximations of Time-Dependent Nonlinear Partial Differential Equations using Galerkin Optimal Auxiliary Function Method

The purpose of this research work is to employ the Optimal Auxiliary Function Method (OAFM) for obtaining numerical approximations of time-dependent nonlinear partial differential equations (PDEs) that arise in many disciplines of science and engineering. The initial and first approximations of parabolic nonlinear PDEs associated with initial conditions have been generated by utilizing this method. Then the Galerkin method is applied to estimate the coefficients that remain unknown. Finally, the values of the coefficients generated by the Galerkin method have been inserted into the first approximation. In each example, all numerical computations and corresponding absolute errors are provided in schematic and tabular representations. The rate of convergence attained by the proposed method is depicted in tabular form

math.NA↗

arXiv2023

Numerical solutions of a class of second order boundary value problems on using Bernoulli Polynomials

The aim of this paper is to find the numerical solutions of the second order linear and nonlinear differential equations with Dirichlet, Neumann and Robin boundary conditions. We use the Bernoulli polynomials as linear combination to the approximate solutions of 2nd order boundary value problems. Here the Bernoulli polynomials over the interval [0, 1] are chosen as trial functions so that care has been taken to satisfy the corresponding homogeneous form of the Dirichlet boundary conditions in the Galerkin weighted residual method. In addition to that the given differential equation over arbitrary finite domain [a, b] and the boundary conditions are converted into its equivalent form over the interval [0, 1]. All the formulas are verified by considering numerical examples. The approximate solutions are compared with the exact solutions, and also with the solutions of the existing methods. A reliable good accuracy is obtained in all cases.

math.NA↗

arXiv2013

Numerical Solutions of Fredholm Integral Equations Using Bernstein Polynomials

In this paper, Bernstein piecewise polynomials are used to solve the integral equations numerically. A matrix formulation is given for a non-singular linear Fredholm Integral Equation by the technique of Galerkin method. In the Galerkin method, the Bernstein polynomials are used as the approximation of basis functions. Examples are considered to verify the effectiveness of the proposed derivations, and the numerical solutions guarantee the desired accuracy.

math.NA↗

arXiv2013

On Comparison between Evolutionary Programming Network-based Learning and Novel Evolution Strategy Algorithm-based Learning

This paper presents two different evolutionary systems - Evolutionary Programming Network (EPNet) and Novel Evolutions Strategy (NES) Algorithm. EPNet does both training and architecture evolution simultaneously, whereas NES does a fixed network and only trains the network. Five mutation operators proposed in EPNet to reflect the emphasis on evolving ANNs behaviors. Close behavioral links between parents and their offspring are maintained by various mutations, such as partial training and node splitting. On the other hand, NES uses two new genetic operators - subpopulation-based max-mean arithmetical crossover and time-variant mutation. The above-mentioned two algorithms have been tested on a number of benchmark problems, such as the medical diagnosis problems (breast cancer, diabetes, and heart disease). The results and the comparison between them are also presented in this paper.

cs.NE↗