A Computational Approach to a Mathematical Model of Climate Change Using Heat Sources and Diffusion

The present work aims to extend the climate change energy balance models using a heat source. An ordinary differential equations (ODEs) model is extended to a partial differential equations (PDEs) model using the effects of diffusion over the spatial variable. In addition, numerical schemes are presented using the Taylor series expansions. For the climate change model in the form of ODEs, a comparison of the presented scheme is made with the existing Trapezoidal method. It is found that the presented scheme converges faster than the existing scheme. Also, the proposed scheme provides fewer errors than the existing scheme. The PDEs model is also solved with the presented scheme, and the results are displayed in the form of different graphs. The impact of the climate feedback parameter, the heat uptake parameter of the deep ocean, and the heat source parameter on global mean surface temperature and deep ocean temperature is also portrayed. In addition, these recently developed techniques exhibit a high level of predictability. Doi: 10.28991/CEJ-2022-08-07-04 Full Text: PD

Numerical Schemes for Fractional Energy Balance Model of Climate Change with Diffusion Effects

This study aims to propose numerical schemes for fractional time discretization of partial differential equations (PDEs). The scheme is comprised of two stages. Using von Neumann stability analysis, we ensure the robustness of the scheme. The energy balance model for climate change is modified by adding source terms. The local stability analysis of the model is presented. Also, the fractional model in the form of PDEs with the effect of diffusion is given and solved by applying the proposed scheme. The proposed scheme is compared with the existing scheme, which shows a faster convergence of the presented scheme than the existing one. The effects of feedback, deep ocean heat uptake, and heat source parameters on global mean surface and deep ocean temperatures are displayed in graphs. The current study is cemented by the fact-based popular approximations of the surveys and modeling techniques, which have been the focus of several researchers for thousands of years.Mathematics Subject Classification:65P99, 86Axx, 35Fxx. Doi: 10.28991/ESJ-2023-07-03-011 Full Text: PD

∈φ-contraction and some fixed point results via modified ω-distance mappings in the frame of complete quasi metric spaces and applications

In this Article, we introduce the notion of an ∈φ-contraction which based on modified ω-distance mappings and employ this new definition to prove some fixed point result. Moreover, we introduced an interesting example and an application to highlight the importance of our work

Online statistical hypothesis test for leak detection in water distribution networks

This paper aims at improving the operation of the water distribution networks (WDN) by developing a leak monitoring framework. To do that, an online statistical hypothesis test based on leak detection is proposed. The developed technique, the so-called exponentially weighted online reduced kernel generalized likelihood ratio test (EW-ORKGLRT), is addressed so that the modeling phase is performed using the reduced kernel principal component analysis (KPCA) model, which is capable of dealing with the higher computational cost. Then the computed model is fed to EW-ORKGLRT chart for leak detection purposes. The proposed approach extends the ORKGLRT method to the one that uses exponential weights for the residuals in the moving window. It might be able to further enhance leak detection performance by detecting small and moderate leaks. The developed method’s main advantages are first dealing with the higher required computational time for detecting leaks and then updating the KPCA model according to the dynamic change of the process. The developed method’s performance is evaluated and compared to the conventional techniques using simulated WDN data. The selected performance criteria are the excellent detection rate, false alarm rate, and CPU time.Peer ReviewedPostprint (author's final draft

A Controlled Contraction Principle in Partial S-Metric Spaces

In this paper, we introduce the notion of a partially a−contractive self mapping and prove the existence and uniqueness of a fixed point for such mapping. Our results improve and generalize many results in S-metric spaces

Lp-potentials on infinite networks

Based on the existence of discrete Lp− subharmonic functions, a classification of infinite networks is carried out

Common Fixed Point under Nonlinear Contractions on Quasi Metric Spaces

We introduce in this article the notion of ( ψ , ϕ ) - quasi contraction for a pair of functions on a quasi-metric space. We also investigate the existence and uniqueness of the fixed point for a couple functions under that contraction

Computational Analysis of MHD Nonlinear Radiation Casson Hybrid Nanofluid Flow at Vertical Stretching Sheet

The stagnation point flow of unsteady compressible Casson hybrid nanofluid flow over a vertical stretching sheet was analyzed. The comparative study of Yamada Ota, Tiwari Das, and Xue hybrid nanofluid models was performed. The Lorentz force was applied normal to flow directions. The effect of nonlinear radiation was studied. We considered the SWCNT (signal wall carbon nanotube) and MWCNT (multi-wall carbon nanotube) with base liquid (water). Under the flow suppositions, a mathematical model was settled by means of boundary layer approximations in terms of partial differential equations. The suitable transformation was developed by using the lie symmetry method. Partial differential equations were transformed into ordinary differential equations by suitable transformations. The dimensionless system was elucidated through a numerical technique named bvp4c. The impacts of pertinent flow parameters on skin friction, Nusselt number, and temperature and velocity distributions were depicted through tabular form as well as graphical form. In this study, the Yamada Ota model achieved a higher heat transfer rate compared to the Tiwari Das and Xue hybrid nanofluid models. The skin friction (CfxRe−1/2) increased and temperature gradient (NuxRe−1/2) declined due to the increment of solid nanoparticle concentration (ϕ2). Physically, skin friction increased because the higher values of the solid nanoparticles increased resistance to the fluid motion

Predictor–Corrector Scheme for Electrical Magnetohydrodynamic (MHD) Casson Nanofluid Flow: A Computational Study

The novelty of this paper is to propose a numerical method for solving ordinary differential equations of the first order that include both linear and nonlinear terms (ODEs). The method is constructed in two stages, which may be called predictor and corrector stages. The predictor stage uses the dependent variable’s first- and second-order derivative in the given differential equation. In literature, most predictor–corrector schemes utilize the first-order derivative of the dependent variable. The stability region of the method is found for linear scalar first-order ODEs. In addition, a mathematical model for boundary layer flow over the sheet is modified with electrical and magnetic effects. The model’s governing equations are expressed in partial differential equations (PDEs), and their corresponding dimensionless ODE form is solved with the proposed scheme. A shooting method is adopted to overcome the deficiency of the scheme for solving only first-order boundary value ODEs. An iterative approach is also considered because the proposed scheme combines explicit and implicit concepts. The method is also compared with an existing method, producing faster convergence than an existing one. The obtained results show that the velocity profile escalates by rising electric variables. The findings provided in this study can serve as a helpful guide for investigations into fluid flow in closed-off industrial settings in the future

Design of Finite Difference Method and Neural Network Approach for Casson Nanofluid Flow: A Computational Study

To boost productivity, commercial strategies, and social advancement, neural network techniques are gaining popularity among engineering and technical research groups. This work proposes a numerical scheme to solve linear and non-linear ordinary differential equations (ODEs). The scheme’s primary benefit included its third-order accuracy in two stages, whereas most examples in the literature do not provide third-order accuracy in two stages. The scheme was explicit and correct to the third order. The stability region and consistency analysis of the scheme for linear ODE are provided in this paper. Moreover, a mathematical model of heat and mass transfer for the non-Newtonian Casson nanofluid flow is given under the effects of the induced magnetic field, which was explored quantitatively using the method of Levenberg–Marquardt back propagation artificial neural networks. The governing equations were reduced to ODEs using suitable similarity transformations and later solved by the proposed scheme with a third-order accuracy. Additionally, a neural network approach for input and output/predicted values is given. In addition, inputs for velocity, temperature, and concentration profiles were mapped to the outputs using a neural network. The results are displayed in different types of graphs. Absolute error, regression studies, mean square error, and error histogram analyses are presented to validate the suggested neural networks’ performance. The neural network technique is currently used on three of these four targets. Two hundred points were utilized, with 140 samples used for training, 30 samples used for validation, and 30 samples used for testing. These findings demonstrate the efficacy of artificial neural networks in forecasting and optimizing complex systems