A numerical algorithm for solving one-dimensional parabolic convection-diffusion equation. Issue 1 (31st December 2023)

• Record Type: Journal Article
• Authors: Koç, Dilara Altan; Öztürk, Yalçın; Gülsu, Mustafa
• Is Part Of: Journal of Taibah University for science. Volume 17:Issue 1(2023)
• Publication Date: 2023-12-31
• Subjects: Partial differential equation -- 1D parabolic convection–diffusion equation -- finite difference method -- Von Neumann stability analysis -- consistency -- convergence; 65M06 -- 65M12; Science -- Periodicals; Science; Periodicals; 505
• DOI: 10.1080/16583655.2023.2204808
• Languages: English
• ISSNs: 1658-3655

Abstract

Abstract : A numerical method for solving one-dimensional (1D) parabolic convection–diffusion equation is provided. We consider the finite difference formulas with five points to obtain a numerical method. The proposed method converts the given equation, domain, and time interval into a discrete form. The numerical values of the solution are approximated by solving algebraic equations containing finite differences and values at these discrete points. The consistency, stability and convergence are investigated. On the other hand, some numerical examples illustrate the validity and applicability of the method. Finally, the numerical results are compared with the finite difference scheme's three points.