A new characteristic numerical approach with evolutionary residual error analysis to nonlinear boundary value problems occurring in heat and mass transfer via combinatoric Mittag-Leffler polynomial. (2nd November 2022)

• Record Type: Journal Article
• Authors: Kürkçü, Ömür Kıvanç; Sezer, Mehmet
• Is Part Of: Numerical heat transfer. Volume 82:Number 9(2022)
• Page Start: 561
• Page End: 575
• Publication Date: 2022-11-02
• Subjects: Error analysis -- heat and mass transfer -- matrix-collocation method -- Mittag-Leffler polynomial; 65L60 -- 34B15 -- 80M22; Heat -- Transmission -- Measurement -- Periodicals; Mass transfer -- Measurement -- Periodicals; Numerical analysis -- Periodicals; 621.4022
• DOI: 10.1080/10407782.2022.2079838
• Languages: English
• ISSNs: 1040-7782

Abstract

Abstract: This study focuses on new numerical approach to the solutions of nonlinear boundary value problems occurring in heat and mass transfer, constructing a matrix-combinatorial method collocated by the Chebyshev-Lobatto points and based on the Mittag-Leffler polynomial. For the first time, a matrix-collocation method is coupled with a combinatoric polynomial. In view of this combination, the method converts the linear and nonlinear terms to the matrix forms and then gathers them to a fundamental matrix equation. In addition to the novelty, an inventive nonlinear residual error analysis of general type is firstly theorized and adapted for improving the solutions to the problems in question and also, it allows to regard the nonlinear terms as an operator in calculations. The obtained solutions are thereby corrected. Numerical and graphical illustrations are provided to scrutinize the accuracy, productivity and comparability of the method. Upon evaluations of all these tasks, one can admit that the method is comprehensible, consistent and easily programmable.