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Article

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Title

Robust iterative spectral algorithms for smooth solutions of time-fractional nonlinear diffusion problems and convergence analysis

Authors

[ 1 ] Instytut Analizy Konstrukcji, Wydział Inżynierii Lądowej i Transportu, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[2.7] Civil engineering, geodesy and transport

Year of publication

2024

Published in

Computers & Mathematics with Applications

Journal year: 2024 | Journal volume: vol. 175

Article type

scientific article

Publication language

english

Keywords
EN
  • Vieta-Lucas polynomials
  • Finite difference method
  • Fractional calculus
  • Allen Cahn problem
  • Spectral method
Abstract

EN Nonlinear time-fractional diffusion problems, a significant class of parabolic-type problems, appear in various diffusion phenomena that seem extensively in nature. Such physical problems arise in numerous fields, such as phase transition, filtration, biochemistry, and dynamics of biological groups. Because of its massive involvement, its accurate solutions have become a challenging task among researchers. In this framework, this article proposed two operational-based robust iterative spectral schemes for accurate solutions of the nonlinear time-fractional diffusion problems. Temporal and spatial variables are approximated using Vieta-Lucas polynomials, and derivative operators are approximated using novel operational matrices. The approximated solution, novel operational matrices, and uniform collection points convert the problem into a system of nonlinear equations. Here, two robust methods, namely Picard's iterative and Newton's, are incorporated to tackle a nonlinear system of equations. Some problems are considered in authenticating the present methods' accuracy, credibility, and reliability. An inclusive comparative study demonstrates that the proposed computational schemes are effective, accurate, and well-matched to find the numerical solutions to the problems mentioned above. The proposed methods improve the accuracy of numerical solutions from 27 % to 100 % when M > 2 as compared to the existing results. The suggested methods' convergence, error bound, and stability are investigated theoretically and numerically.

Date of online publication

29.10.2024

Pages (from - to)

487 - 508

DOI

10.1016/j.camwa.2024.10.015

URL

https://www.sciencedirect.com/science/article/pii/S0898122124004607?dgcid=coauthor

Ministry points / journal

140

Impact Factor

2,9 [List 2023]

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