Journals: Abdelhafid Boussouf University Center of Mila, Algeria
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Numerical solution of some class of differential equations by Galerkin method utilizing Boubaker wavelets: Galerkin method with Boubaker wavelets
No full textThis paper proposes a Galerkin method based on Boubaker wavelets (BWGM) for the numerical solution of a class of differential equations. The method employs Boubaker wavelets as both weight functions and basis elements to construct approximate solutions. The accuracy of the proposed method is evaluated by comparing numerical results with exact solutions and with existing schemes such as the Galerkin method using Fibonacci and Gegenbauer wavelets. Several examples are provided to demonstrate the validity and applicability of the method. The results indicate that BWGM yields high accuracy with minimal absolute error, making it an efficient tool for solving linear, singular, and nonlinear boundary value problems
A practical approach to fixed point theory in partial-metric spaces using simulation functions: Fixed point theory in partial-metric spaces
No full textThis paper investigates coincidence point results for self-mappings in partial-metric spaces via simulation functions. By introducing a generalized contraction condition involving a simulation function and an auxiliary mapping , we establish sufficient conditions for the existence and uniqueness of coincidence points and common fixed points. Our approach not only unifies several existing fixed point theorems in the literature but also provides a genuine extension by weakening conventional contraction assumptions. The theoretical findings are illustrated by a concrete example in a nonstandard partial-metric space setting, confirming the applicability and effectiveness of the proposed framework. As a special case, our results recover and generalize recent fixed point theorems in both metric and partial-metric spaces
A comparative study of analytical and numerical methods for solving systems of nonlinear Volterra integral equations with applications : Comparative study of methods for nonlinear Volterra equations
No full textThis paper presents a detailed comparison of three relatively recent methods for the numerical solution of systems of Nonlinear Volterra Integral Equations of the second kind (NVIEs-II): the Modified Adomian Decomposition Method (MADM), the Hussein-Jassim Method (H-JM), and the Cubic Non-Polynomial Spline Function Method (CNPSFM). The objective of this study is to evaluate the performance of these methods in terms of accuracy, convergence, and numerical stability. To achieve this, all three methods are applied to standard benchmark problems with known exact solutions, enabling quantitative assessment. The numerical results reveal distinct performance characteristics for each method. Both MADM and H-JM demonstrate excellent performance, yielding solutions with high accuracy and very low errors, occasionally approaching machine precision. MADM exhibits rapid convergence, while H-JM provides robust numerical stability and ease of implementation. CNPSFM displays good numerical stability and accurately captures the overall solution behavior; however, it produces relatively larger errors, particularly as the integration interval lengthens. This comparison concludes that the optimal choice among these methods is highly problem-specific. MADM and H-JM are best suited for high-precision applications requiring analytical insight (e.g., quantum mechanics or population dynamics), whereas CNPSFM remains viable for applications prioritizing solution smoothness over absolute accuracy. This study provides practical, evidence-based recommendations to assist researchers and engineers in selecting appropriate solvers for real-world systems modeled by NVIEs-II. Future research should extend these methods to systems with singularities and/or delays, which have been underexplored in the current literature. Another promising direction involves developing hybrid approaches that integrate artificial neural networks with traditional computational solvers
Bifurcation analysis and optimal control in a predator-prey-infection model with additional food
Full text linkWe propose and analyze a three-dimensional eco-epidemiological model involving susceptible and infected prey and predators, in which the predators are supplemented with a constant externally supplied food supply. The model incorporates nonlinear disease transmission and predator feeding saturation through a generalized Holling type II functional response. We investigate the system\u27s dynamics analytically and numerically by examining the existence and stability of equilibria, as well as Hopf, transcritical, and saddle-node bifurcations. One- and two-parameter bifurcation analyses reveal rich dynamics, including limit cycles, period doubling, and chaotic oscillations. Our findings indicate that disease transmission can destabilize the system, while the inclusion of additional food enhances stability and can suppress chaos.Furthermore, we extend the model by introducing a time-dependent optimal control variable representing additional food supply, and derive an optimal strategy using Pontryagin\u27s Maximum Principle. Numerical simulations show that optimal control effectively reduces disease prevalence and stabilizes population dynamics. This study highlights the potential of ecological interventions, such as strategic food supplementation, in regulating complex eco-epidemiological systems
Forecasting Algerian time series: a comparative study of ANN and SARIMA models: Forecasting Algerian time series
No full textAccurate time series forecasting is essential for informed decision-making in economic planning, financial management, and environmental monitoring. Traditional linear models such as the Seasonal Autoregressive Integrated Moving Average (SARIMA) are widely used but often fail to capture the nonlinear and complex dynamics inherent in many real-world datasets. In recent years, Artificial Neural Networks (ANNs) have emerged as a powerful alternative, capable of modeling such complexities without relying on rigid assumptions. This study applies ANN models to three Algerian time series: Gross Domestic Product (GDP), the US Dollar Algerian Dinar (USD/DZD) exchange rate, and monthly average temperature. The forecasting performance of ANN models is benchmarked against SARIMA models. Empirical results demonstrate that ANNs consistently outperform SARIMA models in terms of predictive accuracy across all datasets, highlighting their robustness and adaptability in diverse forecasting contexts
Approximate solution of linear Volterra-Fredholm integral equations via exponential spline function
Full text linkThis paper presents a novel numerical scheme for solving linear Volterra-Fredholm integral equations (V-FIEs) of the second kind, utilizing exponential spline functions (ESFs) in combination with fractional derivatives. The method simplifies computational implementation by converting the original integral equation into a matrix system. To prove the precision and stability of the suggested approach, a thorough convergence analysis is carried out. Numerical experiments, backed by graphical representations, validate the method\u27s high accuracy and computational efficiency, even with a limited number of subintervals. All simulations and visualizations are implemented using Python. The results indicate that the suggested ESF approach performs noticeably better than traditional methods
An L2-stability analysis of a θ-scheme for a class of nonlinear parabolic variational inequalities of obstacle type: L2 Stability of a θ-scheme for parabolic PVIs
No full textThis paper analyzes the stability of a fully discrete finite element approximation for a class of nonlinear parabolic variational inequalities of obstacle type. The temporal discretization is based on a θ-scheme. We derive a stability condition for the scheme that depends critically on the parameter θ. We prove that the method is unconditionally stable in the L2-norm for θ in [1/2,1]. For θ in [0,1/2), we establish a precise Courant-Friedrichs-Lewy (CFL)-type condition, Delta t<=2gγ/(L2(1-2θ)), where γ is the coercivity constant and L is the Lipschitz constant of the nonlinear source term. The analysis is based on a careful choice of test functions in the variational inequality and by deriving sharp estimates of the associated bilinear form
Uncertainty and specification challenges in exchange rates modeling under Bayesian model averaging: Uncertainty & Specification in BMA Exchange Rate Models
No full textTraditional econometric models often struggle to capture the complexities and uncertainties inherent in exchange rate movements. This study investigates the dynamic relationship between the Nigerian Naira exchange rate and key economic variables using Bayesian Model Averaging (BMA), offering a robust framework to address model uncertainty and specification challenges. By integrating multiple predictors, BMA enhances forecasting accuracy, providing valuable insights for policymakers, investors and businesses navigating Nigeria\u27s volatile economic landscape. Analysing exchange rate movements from 2007 to 2021, the study assesses BMA\u27s effectiveness compared to traditional models, particularly in capturing non-linear relationships and time-varying volatility. Findings reveal that capital expenditure and the money supply are the most significant determinants of exchange rate fluctuations: capital expenditure negatively affects the exchange rate, while increased money supply leads to currency appreciation. These results highlight the potential of BMA to refine economic forecasts and improve decision-making in Nigeria\u27s financial and policy sectors
On some properties of k-circulant matrices with the generalized Pell-Padovan numbers
Full text linkIn this paper, we investigate the properties of the -circulant matrix generated by the generalized Pell--Padovan numbers. We derive explicit formulas for the sum of entries, the maximum column sum norm (), the maximum row sum norm (), the Frobenius (Euclidean) norm (), as well as the eigenvalues and determinant of this matrix. Furthermore, we establish upper and lower bounds for its spectral norm (), thereby providing a comprehensive analysis of the structural andspectral characteristics of the -circulant matrix associated with thegeneralized Pell--Padovan sequence
The Galerkin method for the numerical solution of some class of differential equations by utilizing Gegenbauer wavelets
No full textMany differential equations that emerge from modeling physical phenomena do not always possess well-known analytical solutions. Additionally, wavelets have attracted considerable attention from both theoretical and applied researchers in recent decades. In this study, we introduce the Galerkin method for numerically solving a specific class of differential equations by employing Gegenbauer wavelets (GWGM). In this approach, Gegenbauer wavelets serve as weight functions and are treated as basis elements, enabling us to derive the numerical solution. The numerical solutions obtained through this method are compared with several existing methods and the exact solution. Various examples are presented to demonstrate the effectiveness and applicability of the proposed technique