An explicit unconditionally stable scheme: application to diffusive Covid-19 epidemic model

Yasir Nawaz; Muhammad Shoaib Arif; Kamaleldin Abodayeh; Wasfi Shatanawi

doi:10.1186/s13662-021-03513-7

An explicit unconditionally stable scheme: application to diffusive Covid-19 epidemic model

Adv Differ Equ. 2021;2021(1):363. doi: 10.1186/s13662-021-03513-7. Epub 2021 Aug 3.

Authors

Yasir Nawaz¹, Muhammad Shoaib Arif¹, Kamaleldin Abodayeh², Wasfi Shatanawi^{2

3

4}

Affiliations

¹ Department of Mathematics, Air University, PAF Complex E-9, Islamabad, 44000 Pakistan.
² Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia.
³ Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402 Taiwan.
⁴ Department of Mathematics, Hashemite University, Zarqa, Jordan.

Abstract

An explicit unconditionally stable scheme is proposed for solving time-dependent partial differential equations. The application of the proposed scheme is given to solve the COVID-19 epidemic model. This scheme is first-order accurate in time and second-order accurate in space and provides the conditions to get a positive solution for the considered type of epidemic model. Furthermore, the scheme's stability for the general type of parabolic equation with source term is proved by employing von Neumann stability analysis. Furthermore, the consistency of the scheme is verified for the category of susceptible individuals. In addition to this, the convergence of the proposed scheme is discussed for the considered mathematical model.

Keywords: Conditionally positivity preserving; Convergence conditions; Diffusive COVID-19 model; Proposed scheme; Stability.