Approximation of 3D convection diffusion equation using DQM based on modified cubic trigonometric B-splines

Article type: Research Article

Authors: Tamsir, Mohammad^a | Dhiman, Neeraj^{b; *} | Gill, F.S.^c | Robin, ^b

Affiliations: [a] Department of Mathematics, Jazan University, Jazan, Saudi Arabia | [b] Department of Mathematics, Graphic Era Hill University, Dehradun, India | [c] Department of Physics, Graphic Era (deemed to be) University, Dehradun, India

Correspondence: [*] Corresponding author: Neeraj Dhiman, Graphic Era Hill University, Dehradun, India. E-mail: neeraj.dhiman1@gmail.com.

Abstract: This paper presents an approximate solution of 3D convection diffusion equation (CDE) using DQM based on modified cubic trigonometric B-spline (CTB) basis functions. The DQM based on CTB basis functions is used to integrate the derivatives of space variables which transformed the CDE into the system of first order ODEs. The resultant system of ODEs is solved using SSPRK (5,4) method. The solutions are approximated numerically and also presented graphically. The accuracy and efficiency of the method are validated by comparing the solutions with existing numerical solutions. The stability analysis of the method is also carried out.

Keywords: 3D convection diffusion equation, CTB basis functions, DQM, SSPRK (5, 4), stability analysis

DOI: 10.3233/JCM-200034

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 20, no. 4, pp. 1357-1366, 2020