This study presents a mathematical model incorporating both asymptomatic and symptomatic HIV-infected individuals to analyze the dynamics of HIV/AIDS. expanded offers more comprehensive understanding epidemic's spread. We calculate basic reproduction number (R0) quantify virus's transmission potential. To achieve accurate robust simulations, we introduce Nonstandard Finite Difference Scheme (NSFD). Compared traditional methods like RK-4, NSFD improved dynamical consistency numerical...

We analyze the nonlinear (2+1)-dimensional KdV–mKdV equation with Caputo fractal–fractional operator. Some theoretical features are demonstrated via fixed point results. The solution of considered is studied by composition J-transformation and decomposition method. For validity effectiveness method, two examples suitable initial conditions solved, where best agreements observed. suggested approach verified convergence analysis Picard stability. From simulations obtained results, it noted...

A Hermite based block method (HBBM) is proposed for the numerical solution of second-order non-linear elliptic partial differential equations (PDEs). The development was accomplished through methodology interpolation and collocation procedures. method’s analysis reveals that it satisfied requirements a technique to be convergent. implementation extensively discussed. Five examples originating from physical phenomena are presented, applicability accuracy HBBM established by comparing them...

Entropy generation (EG) in bioconvective nanofluid flows is a phenomenon that occurs due to the presence of nanoparticles and microorganisms within fluid flows. EG leads an increase thermodynamic irreversibility system. Understanding quantifying essential optimize heat transfer processes design efficient systems. Current investigation aims analyze magnetized flow non-Newtonian micropolar type nanofluid. Flow features are modeled considering by Darcy Forchheimer permeable surface stretched...

In this article, a variable step size strategy is adopted in formulating new hybrid block method (VSHBM) for the solution of Kepler problem, which known to be rigid and stiff differential equation. To derive VSHBM, ratio r left same, halved, or doubled order optimize total number steps, minimize formulae stored code, ensure that zero-stable. The formulated by integrating Lagrange polynomial with limits integration selected at special points. article further analyzed stability, order,...

This paper describes a third-derivative hybrid multistep technique (TDHMT) for solving second-order initial-value problems (IVPs) with oscillatory and periodic in ordinary differential equations (ODEs), the coefficients of which are independent frequency <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mfenced open="(" close=")" separators="|"> <mrow> <mtext>omega</mtext> </mrow> </mfenced> </math> step size id="M2"> <mi>h</mi> . research is significant because it has numerous...

The aim of this paper is to study new exact solutions Davey–Stewartson–Kadomtsev–Petviashvili (DSKP) equation. We use modified tanh method along associated with Ricatti results are demonstrated for specific values parameters, which show periodic singular as well nonsingular solitons parameters. Some plotted and presented in 3D density graphs. Mathematica used computation simulations the results, respectively.

Second-order oscillatory problems have been found to be applicable in studying various phenomena science and engineering; this is because these the capabilities of replicating different aspects real world. In research, a new hybrid method shall formulated for simulations second-order with applications physical systems. The proposed using procedure interpolation collocation by adopting power series as basis function. formulating method, off-step points were introduced within interval...

A computational approach with the aid of Linear Multistep Method (LMM) for numerical solution differential equations initial value problems or boundary conditions has appeared several times in literature due to its good accuracy and stability properties. The major objective this article is extend a multistep Partial Differential Equation (PDE) originating from fluid mechanics two-dimensional space conditions, as result importance utility models partial applications, particularly physical...

Abstract Our study explores neutrosophic statistics, an extension of classical and fuzzy to address the challenges data uncertainty. By leveraging accurate measurements auxiliary variable, we can derive precise estimates for unknown population median. The estimators introduced in this research are particularly useful analysing unclear, vague or within realm. Unlike traditional methods that yield single-valued outcomes, our produce ranges, suggesting where parameter is likely be. We present...

Abstract In this paper, we introduce a biparametrized multiplicative integral identity and employ it to establish collection of inequalities for multiplicatively convex mappings. These encompass several novel findings refinements established results. To enhance readers’ comprehension, offer illustrative examples that highlight appropriate choices mappings along with graphical representations. Finally, demonstrate the applicability our results special means real numbers within realm calculus.

This paper aims to present two nonstandard finite difference (NFSD) methods solve an SIR epidemic model. The proposed have important properties such as positivity and boundedness they also preserve conservation law. Numerical comparisons confirm that the accuracy of our method is better than other existing standard second-order Runge–Kutta (RK2) method, Euler some ready-made MATLAB codes.

Over the years, researches have shown that fixed (constant) step-size methods been efficient in integrating a stiff differential system. It has however observed for some systems, non-fixed (variable) are required efficiency and accuracy to be attained. This is because such systems solution components decay rapidly and/or slowly than others over given integration interval. In order curb this challenge, there need propose method can vary step size within defined challenge motivated development...

Allen Cahn (AC) equation is highly nonlinear due to the presence of cubic term and also very stiff; therefore, it not easy find its exact analytical solution in closed form. In present work, an approximate AC has been investigated. Here, we used variational iteration method (VIM) for equation. The obtained results are compared with hyperbolic function traveling wave solution. Results numerical by using finite difference (FDM). Absolute error analysis tables validate series A convergent VIM...

We study, in this paper, the Cauchy problem for matrix factorizations of Helmholtz equation space Rm. Based on constructed Carleman matrix, we find an explicit form approximate solution and prove stability solutions.

Abstract Typhoid fever is a contagious disease that generally caused by bacteria known as Salmonella typhi. This spreads through manure contamination of food or water and infects unprotected people. In this work, our focus to numerically examine the dynamical behavior typhoid nonlinear mathematical model. To achieve objective, we utilize conditionally stable Runge–Kutta scheme order 4 (RK-4) an unconditionally non-standard finite difference (NSFD) better understand continuous The primary...

A Hermite fitted block integrator (HFBI) for numerically solving second-order anisotropic elliptic partial differential equations (PDEs) was developed, analyzed, and implemented in this study. The method derived through collocation interpolation techniques using the polynomial as basis function. interpolated at first two successive points, while occurred all suitably chosen points. major scheme its complementary were united together to form HFBI. analysis of HFBI showed that it had a...

In this paper, two numerical methods for solving the MSEIR model are presented. constructing these methods, non-standard finite difference strategy is used. The new preserve qualitative properties of solution, such as positivity, conservation law, and boundedness. Numerical results presented to express efficiency methods.

In this paper, on the basis of Carleman matrix, we explicitly construct a regularized solution Cauchy problem for matrix factorization Helmholtz's equation in an unbounded two-dimensional domain. The focus paper is regularization formulas solutions to problem. question existence not considered-it assumed priori. At same time, it should be noted that any formula leads approximate all data, even if there no usual classical sense. Moreover, explicit formulas, one can indicate what sense turns...

In this paper, using the construction of Carleman matrix, we explicitly find a regularized solution Cauchy problem for matrix factorizations Helmholtz equation in three-dimensional unbounded domain.

This study aims to develop, analyze and implement an efficient method for approximating two-point boundary value problems of ordinary differential equations. The contains six twelve implicit formulas, respectively, the one-step two-step schemes. continuous approximations, using shifted Chebyshev polynomial as basis function, were obtained via evaluations at three different points on selected method, including two optimized hybrid points. Evaluations carried out four generalized Qualitative...