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All Journal Emerging Science Journal Civil Engineering Journal
Yasir Nawaz
Department of Mathematics, Air University, PAF Complex E-9, Islamabad 44000,
Civil Engineering, Building, Construction & Architecture Environmental Science

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A Computational Approach to a Mathematical Model of Climate Change Using Heat Sources and Diffusion Muhammad Shoaib Arif; Kamaleldin Abodayeh; Yasir Nawaz
Civil Engineering Journal Vol 8, No 7 (2022): July
Publisher : Salehan Institute of Higher Education

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.28991/CEJ-2022-08-07-04

Abstract

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: PDF
Numerical Schemes for Fractional Energy Balance Model of Climate Change with Diffusion Effects Muhammad Shoaib Arif; Kamaleldin Abodayeh; Yasir Nawaz
Emerging Science Journal Vol 7, No 3 (2023): June
Publisher : Ital Publication

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.28991/ESJ-2023-07-03-011

Abstract

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: PDF
A Third-order Two Stage Numerical Scheme and Neural Network Simulations for SEIR Epidemic Model: A Numerical Study Muhammad Shoaib Arif; Kamaleldin Abodayeh; Yasir Nawaz
Emerging Science Journal Vol 8, No 1 (2024): February
Publisher : Ital Publication

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.28991/ESJ-2024-08-01-023

Abstract

This study focuses on the cutting-edge field of epidemic modeling, providing a comprehensive investigation of a third-order two-stage numerical approach combined with neural network simulations for the SEIR (Susceptible-Exposed-Infectious-Removed) epidemic model. An explicit numerical scheme is proposed in this work for dealing with both linear and nonlinear boundary value problems. The scheme is built on two grid points, or two time levels, and is third-order. The main advantage of the scheme is its order of accuracy in two stages. Third-order precision is not only not provided by most existing explicit numerical approaches in two phases, but it also necessitates the computation of an additional derivative of the dependent variable. The proposed scheme's consistency and stability are also examined and presented. Nonlinear SEIR (susceptible-exposed-infected-recovered) models are used to implement the scheme. The scheme is compared with the non-standard finite difference and forward Euler methods that are already in use. The graph shows that the plan is more accurate than non-standard finite difference and forward Euler methods that are already in use. The solution obtained is then looked at through the lens of the neural network. The neural network is trained using an optimization approach known as the Levenberg-Marquardt backpropagation (LMB) algorithm. The mean square error across the total number of iterations, error histograms, and regression plots are the various graphs that can be created from this process. This work conducts thorough evaluations to not only identify the strengths and weaknesses of the suggested approach but also to examine its implications for public health intervention. The results of this study make a valuable contribution to the continuously developing field of epidemic modeling. They emphasize the importance of employing modern numerical techniques and machine learning algorithms to enhance our capacity to predict and effectively control infectious diseases. Doi: 10.28991/ESJ-2024-08-01-023 Full Text: PDF
Co-Authors Kamaleldin Abodayeh Kamaleldin Abodayeh Muhammad Shoaib Arif Muhammad Shoaib Arif Muhammad Shoaib Arif