Stiff systems of ordinary differential equations (ODEs) arise frequently in several areas of applied mathematics, science, and engineering, and their numerical integration requires methods with strong stability characteristics. In this paper, a block extended backward differentiation formula (BEBDF) with a stability control parameter is developed for the numerical solution of stiff systems of ODEs. The proposed method is constructed within the framework of block multistep methods, allowing the simultaneous computation of solution values at several grid points. A free parameter $\rho$ is incorporated into the formulation of the method to regulate and improve its stability behavior. The presen... More >

This study explores the application of the Adomian Decomposition Method (ADM), combined with the Laplace transform, to obtain approximate solutions of the time--fractional Wazwaz--Benjamin--Bona--Mahony (WBBM) equations. These equations, which describe wave phenomena in fluid dynamics within a fractional--time framework, present significant analytical challenges. By integrating the Laplace transform with ADM, a modified technique---referred to as the Laplace Transform Adomian Decomposition Method (LTADM)---is introduced. The time--fractional WBBM equations are solved using LTADM, and three--dimensional solution plots are generated for six different values of the fractional order \( \delta \)... More >

The underpinnings, usage, and capabilities of source code developed to simultaneously compute and display the temporal evolution of quantum-mechanical wavefunctions are described. This computation is done through direct numerical integration of Schrödinger's equation and is limited to one spatial dimension. The source code is freely downloadable for noncommercial, educational purposes. The Schrödinger equation's linearity in facilitating the computations along with important restrictions imposed by the algorithms employed are emphasized. Physical interpretations of the example systems treated are highlighted. Plenty of citations and footnotes are provided---both historical and pedagogical.... More >

In this paper, the concept of the bipolar spherical fuzzy set (BSFS) and its operations is developed. It is proposed as a generalization of fuzzy sets, bipolar fuzzy sets, picture fuzzy sets, and spherical fuzzy sets, allowing uncertain information to be handled more flexibly in the decision-making process. The key objective of this research paper is to introduce a new version of the spherical fuzzy set so called bipolar spherical fuzzy set (BSFS). The bipolar spherical fuzzy set is a new extension of spherical fuzzy sets and picture fuzzy sets. In bipolar spherical fuzzy sets, membership degrees are satisfying the condition \( 0 \leq (s^+)^2(x) + (i^+)^2(x) + (d^+)^2(x) \leq 1 \) and \( 0 \... More >

The initial mathematical model for rabies consists of six compartments representing the human and dog populations: $S_h, I_h, V_h, S_d, I_d, V_d$. To obtain a more realistic description of rabies transmission dynamics, we extend the model by introducing two additional human compartments: Exposed ($E_h$) and Recovered ($R_h$) individuals. The extended system therefore comprises eight compartments: $S_h, E_h, I_h, V_h, R_h, S_d, I_d, V_d$. This extension captures important differences in disease progression, treatment response, and transmission pathways. Within this framework, we examine the positivity and boundedness of solutions, derive the basic reproduction number ($R_0$), analyse the sens... More >

Previous research has focused on formulating cancer treatment strategies within a single-drug framework, which clearly fails to effectively address the practical needs of combination drug therapy in clinical settings. Therefore, this study develops a multi-drug cancer treatment model and conducts strategy design and simulation investigations under hypothetical patient-specific parameters for dual-drug regimens. Based on the previously proposed adaptive threshold strategy and several novel strategies integrating threshold-based and sequential administration patterns, and conducted a parameter search and optimization of upper/lower thresholds was performed to explore the performance improvemen... More >

Rabies remains a serious public health concern, as dog bites account for the majority of human cases. In this study, we develop a comprehensive mathematical model to investigate the dynamics of rabies transmission by incorporating two key intervention strategies: an asymptotic class (\(P\)) and a booster vaccination class (\(B\)). The basic reproduction number (\(R_0\)) is derived as a threshold parameter that governs whether the disease spreads or dies out, based on a system of nonlinear differential equations. A sensitivity analysis of \(R_0\) is conducted to identify the most influential parameters affecting disease transmission. The results indicate that the transmission rate (\(\beta\))... More >

Despite extensive study of max--min problems, convergence analysis for the challenging nonconvex--nonconcave setting remains limited. This paper addresses the convergence analysis of nonconvex--nonconcave max--min problems. A novel analytical framework is developed by employing carefully constructed auxiliary functions and leveraging two-sided Polyak--Łojasiewicz (PL) and Quadratic Growth (QG) conditions to characterize the convergence behavior. Under these conditions, it is shown that the Stochastic Alternating Gradient Descent Ascent (SAGDA) algorithm achieves a convergence rate of $\mathcal{O}\left(1/K\right)$, where $K$ denotes the number of iterations. Notably, this result matches conv... More >