In this study, we have examined a stochastic delay differential equation in one dimension. We employed the Runge-Kutta method along with the method of lines to address the issue, establishing stability analysis and studying the spread of discontinuities. Additionally, we derived a semi-discretization in the temporal domain. Subsequently, the Runge-Kutta method of order four and cubic Hermite Interpolation is derived and numerical examples are illustrated for the theoretical result.

We introduce and examine certain bi-univalent functions subclasses connected polylogarithm function. The convolution of two well-known differential operators define the new differential operator. By utilizing the new differential operator Qnδ,λ we provide some new bi-univalent subclasses and estimate the basic coefficients |a2| and |a3|. Furthermore, specializing some parameters in our primary findings, we show that various fresh results have been obtained. The results of this study will fortify the field’s theoretical foundations and open up fresh avenues for mathematical inquiry and application.

The goal of this research is to create and investigate a new class of sets in microtopological-spaces called micro-minimaḷ-closed-sets and micro-generalized regularminimaḷ-closed sets. are examined for their basic features.

This paper is based on the idea of unique fixed points as the result of weakly contractive maps in the structure of asymmetric b−metric spaces. Moreover, provided to illustrate the broader implications of our results compared.

V-Phenylenic nanotubes VPNTU[l,k] and nanotori VPNTO[l,k] are theoretically predicted carbon-based nanostructures with promising electronic and mechanical properties. While experimental synthesis remains elusive, computational studies suggest they could exhibit exceptional conductivity, strength, and potential applications in electronic and materials science. In this article, the new Revan indices (RI) for molecular graph (MG), line graph (LG) and subdivision graph (SG) of VPNTU [l, k] and VPNTO [l, k] are investigated. By utilizing M-polynomial obtained from MG, LG and SG and MATLAB software coding, calculations and results obtained from research are presented.

This research investigates the application of the Riccati-Bernoulli (R-B) sub-ODE technique to analyze the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) and the three-dimensional Potential Yu-Toda-Sasa-Fukuyama (3D-PYTSF) equations. By integrating traveling wave transformations with the R-B framework, both equations are systematically reduced to algebraic systems. Various soliton solutions, including kink-type, singular, and periodic solutions, are derived. To visualize the physical significance of these solutions, 3D plots, density graphs, and contour diagrams are generated based on appropriate parameter selections. The R-B sub-ODE method proves to be an effective yet straightforward technique for addressing nonlinear partial differential equations (NLPDEs).

Orbital mechanics with perturbation methods gives us a way to look at departures from the idealized Keplerian motion using math. Changes happen because of gravity, uneven mass distributions, air drag, sun radiation pressure, and relativistic corrections. This research looks into mathematical and numerical perturbation methods, focusing on how well they can predict orbital paths and long-term stability. Numerical methods let us directly integrate complex dynamical systems, while analytical methods give closed-form answers for simple changes. A comparison analysis shows the pros, cons, and areas where each one can be used. The study shows that perturbation methods are very important for current astrodynamics, satellite tracking, and mission planning in settings with many bodies.

The quadratically convergent Newton method is a fundamental and significant approach for solving one-variable functions. In order to solve a single minimization issue, we deduce a novel secant type approach in this study that is based on estimating the second derivative information. The convergence of the novel secant type iterative approach is of order two. The provided application examples show that the suggested technique outperforms the Newton method in terms of numerical properties.

In environmental research, challenges with water contamination assessment are generally prevalent. Through data collection, pollution levels in a system may be determined. This is quite challenging and involved; the measurements of what was measured vary from one point to another in every location. The governing equations for a uniform flow pollution dispersion model are used in water quality modeling. The advection-diffusion-reaction equation used in water quality model-ing for a uniform flow stream is a stable pollution dispersion model. This study presents a one-dimensional mathematical model for measuring stream water quality by collocation higher order Legendre polynomial functions. A water pol-lutant concentration can be approximated using the collocation method. A related water quality quantification method may also be employed with the suggested mathematical simulation to approximate the solution.

In this manuscript, we introduce the idea of operation approach on on spherical fuzzy soft topology (𝒮𝓕𝒮 𝒯) and analyse its characteristics in spherical fuzzy soft topological space. Also, we define 𝒮𝓕𝒮 g~-regular space and 𝒮𝓕𝒮 g~ regular operation in 𝒮𝓕𝒮 𝒯𝒮 and study certain results using 𝒮𝓕𝒮 g~-regular space and 𝒮𝓕𝒮 g~-regular operation. Using operation on 𝒮𝓕𝒮 topology, we bring forth the topological operators like 𝒮𝓕𝒮 g~-closure and 𝒮𝓕𝒮 g~-interior and analyse their characteristics. As an application of operation approach on 𝒮𝓕𝒮 topology, we present a decision making algorithm and provide an illustration. We also develop a python program for the proposed algorithm.