JAEM 2026, Vol 16, No 9

Symbolic differentiation algorithms for hyperbolic perturbation problems with Neumann conditions using asymptotic formulas and uniform difference schemes

2026-09-09T09:32:51Z

Symbolic differentiation algorithms for hyperbolic perturbation problems with Neumann conditions using asymptotic formulas and uniform difference schemes Ashyralyev, Allaberen; Yıldırım, Özgür In this paper, we investigate asymptotic formulas and ε-uniform difference schemes for the numerical solution of perturbation problems. Unfortunately, both of these numerical methods involving sine and cosine fitting operator functions, which depend on ρ (ρ = τ /ε, ε small parameter and τ stepsize in t), are highly challenging with the realization to use symbolic differential algorithms. We present a symbolic differentiation algorithm developed for the numerical solution of hyperbolic perturbation problems with Neumann boundary conditions, employing asymptotic formulas and ε-uniform difference schemes. The symbolic differential algorithms are implemented by Matlab, and the results of numerical experiments are presented.

A high-order Caputo-based numerical scheme for approximating the one-dimensional time-independent fractional Schrödinger equation

2026-09-09T09:09:00Z

A high-order Caputo-based numerical scheme for approximating the one-dimensional time-independent fractional Schrödinger equation Habibzadeh, Hojjat; Shahriari, Mohammad; Shokri, Ali; Khalsaraei, Mohammad Mehdizadeh The time-independent fractional Schrödinger equation is pivotal for modeling quantum systems exhibiting nonlocal interactions and anomalous dispersion, for which analytical solutions are often intractable. This paper presents a high-order numerical scheme to approximate the solution of the one-dimensional time-independent Schrödinger equation incorporating Caputo fractional derivatives of order α, comprehensively covering the ranges 0 < α ≤ 1 and 1 < α ≤ 2. The core of our approach lies in the development of novel finite difference discretizations. For 0 < α ≤ 1, we employ a second-order weighted-shifted Grünwald approximation to achieve higher accuracy than standard schemes. For 1 < α ≤ 2, a distinct high-order approximation is derived, which is further extended to a fourth-order scheme for enhanced precision. A rigorous theoretical analysis is provided, including a detailed error bound proof that establishes the scheme’s accuracy and stability. We also investigate the convergence rate and the impact of numerical errors on long-term simulations, demonstrating the method’s robustness. The validity and efficiency of the proposed method are confirmed through several numerical examples. The results show excellent agreement with exact solutions in limiting cases (e.g., α → 2) and confirm that the observed convergence orders align with our theoretical predictions. The findings indicate that the developed high-order Caputo-based scheme is a powerful and reliable tool for solving fractional Schrödinger equations, offering significant improvements in accuracy for a wide range of fractional orders.

The Quantile Garch-Distributed Lag (QGDL) framework: a unified model for high-volatility time series

2026-09-09T08:43:20Z

The Quantile Garch-Distributed Lag (QGDL) framework: a unified model for high-volatility time series Mousa, Maryam Jumaa; Hmood, Munaf Yousif The essence of this article is that it has developed the Quantile GARCHDistributed Lag (QGDL) model as a recent and superior model to the QARDL model. Although the QARDL model is only able to deal with asymmetric relationships in the quartiles and the assumption of homoscedasticity, our model is able to address this weakness using the simultaneous volatility clustering. The model that we propose is the most effective and correct in estimating the parameters in cases of changing conditional variance with time, which makes it the most appropriate measure to use in the analysis of extremely volatile financial time series.

Ensitivity and optimizing dengue control in a two-time-delay transmission model

2026-09-09T06:58:42Z

Ensitivity and optimizing dengue control in a two-time-delay transmission model Prakash Raj, Murugadoss; Venkatesh, Ambalarajan; Kumar, Karuppusamy Arun; Manivel, M. This study presents a detailed analysis of a dengue transmission model that incorporates two biologically motivated time delays, representing the intrinsic and extrinsic incubation periods in host-vector interactions. Based on a vector-host framework, the model examines the influence of key transmission parameters through sensitivity analysis and contour plots. The basic reproduction number R0 is analytically derived and assessed for its dependence on epidemiologically significant factors. To curb disease spread, an optimal control problem is formulated by introducing three time-dependent control strategies: personal protection, vector control, and vector targeting efficiency. Employing Pontryagin’s Maximum Principle, the necessary conditions for optimality are established. Numerical simulations under various delay scenarios reveal that optimal control strategies significantly reduce both human and vector infections. However, the presence and magnitude of delays affect the speed and efficacy of intervention. The findings emphasize the critical role of accounting for biological delays and implementing targeted controls in designing effective dengue prevention strategies.