The novelty of this paper is to propose a numerical method for solving ordinary differential equations the first order that include both linear and nonlinear terms (ODEs). constructed in two stages, which may be called predictor corrector stages. stage uses dependent variable’s first- second-order derivative given equation. In literature, most predictor–corrector schemes utilize first-order variable. stability region found scalar ODEs. addition, mathematical model boundary layer flow over...

This study reveals the extension of a mathematical model heat and mass transfer fluid flow over sheet by incorporating effect non-linear mixed convection. The governing equations phenomena are expressed as partial differential (PDEs). Similarity transformations employed to get dimensionless set boundary value problems. Most existing relevant literature some solver solve equations, but this implements finite element method tackle is based on Galerkin approach. For verifications obtained...

Stochastic simulations enable researchers to incorporate uncertainties beyond numerical discretization errors in computational fluid dynamics (CFD). Here, the authors provide examples of stochastic incompressible flows and solutions for validating these newly emerging modeling methods. A scheme is constructed finding parabolic equations. The second-order accurate time constant coefficient Wiener process term. stability analysis also provided. applied dimensionless heat mass transfer model...

It is imperative to investigate the proposed computational scheme for resolution of two-dimensional partial differential equations that result from non-Newtonian nanofluid flow over flat and oscillatory sheets, taking into account effects magnetic field chemical reactions, as it designed address stochasticity, unstable conditions, Maxwellian behaviour. Consequently, offers valuable insights dynamics nanofluids. A stochastic suggested (PDEs) caused by sheets in presence a reaction effects....

Abstract Researchers can incorporate uncertainties in computational fluid dynamics (CFD) that go beyond the inaccuracies caused by numerical discretization thanks to stochastic simulations. This study confirms validity of current modeling tools providing examples simulations conjunction with solutions for incompressible flows. A technique solving deterministic and models is developed this work. Our approach employs Euler‐Maruyama method modeling, representing a version third‐order...

Abstract This contribution is concerned with constructing a fractional explicit‐implicit numerical scheme for solving time‐dependent partial differential equations. The proposed has the advantage over some existing explicit in providing better stability region. But it one of its limitations being conditionally stable, even having implicit stage. For spatial discretization, fourth‐order compact considered. and convergence respectively scalar parabolic equation system equations are given. sake...

This study aims to propose numerical schemes for fractional time discretization of partial differential equations (PDEs). The scheme is comprised two stages. Using von Neumann stability analysis, we ensure the robustness scheme. energy balance model climate change modified by adding source terms. local analysis presented. Also, in form PDEs with effect diffusion given and solved applying proposed compared existing scheme, which shows a faster convergence presented than one. effects feedback,...

This contribution proposes two third-order numerical schemes for solving time-dependent linear and non-linear partial differential equations (PDEs). For spatial discretization, a compact fourth-order scheme is deliberated. The stability of the proposed set scalar equation, whereas its convergence specified system parabolic equations. applied to equation systems comprises governing heat mass transfer magnetohydrodynamics (MHD) mixed convective Casson nanofluid flow across oscillatory sheet...

To boost productivity, commercial strategies, and social advancement, neural network techniques are gaining popularity among engineering technical research groups. This work proposes a numerical scheme to solve linear non-linear ordinary differential equations (ODEs). The scheme’s primary benefit included its third-order accuracy in two stages, whereas most examples the literature do not provide stages. was explicit correct third order. stability region consistency analysis of for ODE...

This study introduces a novel and versatile fractal finite difference scheme designed to address unsteady flow challenges in quantum calculus over flat oscillatory sheets. Motivated by the need advance our understanding of nanofluid dynamics, particularly heat mass transportation, this research aims bridge existing gaps contribute improving computational methodologies. Our approach involves two-stage incorporating explicit implicit methods, focusing on q-derivatives for spatial terms within...

Abstract Nowadays, Casson fluid has been broadly used in plasma, sweetie, coffee, and several polymer solutions, for which the analysis of its essential flow transport heat devices multifaceted surroundings is energetic importance. One exclusive specific exceptional aspects yield stress. The works similarly to a dense when shear power less than stress, whereas it collapses arises once above This benefits describing fluids with unbounded viscosity at nil rate rate, fascinated greatly...

Climate change, primarily driven by CO2 emissions from energy and non-energy sectors, necessitates effective mitigation strategies. This study develops a stochastic diffusive model to capture the complex dynamics of concentration, human population growth, production. The objectives are enhance predictive accuracy existing models incorporating diffusion effects variability, offering insights for sustainable environmental policies. A novel numerical scheme, an extension Euler-Maruyama...

The main contribution of this article is to propose a compact explicit scheme for solving time-dependent partial differential equations (PDEs). proposed has an advantage over the corresponding implicit find solutions nonlinear and linear convection–diffusion type because existing fails obtain solution. In addition, present provides fourth-order accuracy in space second-order time, constructed on three grid points time levels. It multistep conditionally stable, while developed levels...

Abstract A third-order numerical scheme is proposed for solving fractional partial differential equations (PDEs). The first explicit stage can converge fast, and the second implicit responsible enlarging stability region. fourth-order compact employed to discretize spatial derivative terms. of given standard parabolic equation, whereas convergence system equations. Mathematical models heat mass transfer Stokes problems using Dufour Soret effects are in a set linear nonlinear PDEs. Later on,...

The recent study was concerned with employing the finite element method for heat and mass transfer of MHD Maxwell nanofluid flow over stretching sheet under effects radiations chemical reactions. Moreover, viscous dissipation porous plate were considered. mathematical model described in form a set partial differential equations (PDEs). Further, these PDEs transformed into nonlinear ordinary (ODEs) using similarity transformations. Rather than analytical integrations, numerical integration...

The main aim of this contribution is to construct a numerical scheme for solving stochastic time-dependent partial differential equations (PDEs). This has the advantage problems with positive solutions. provides conditions obtaining solutions, which existing Euler–Maruyama method cannot do. In addition, it more accurate than non-standard finite difference (NSFD) method. Theoretically, suggested current NSFD method, and its stability consistency analysis are also shown. applied linear scalar...