Work

Spectral collocation approach for solving the time-fractional Kuramoto-Sivashinsky equation using the Fibonacci coefficient polynomials

Year: 2025

Type: article

Abstract: This work presents an algorithm that applies the typical collocation method to solve the time-fractional Kuramoto–Sivashinsky equation (TFKSE). Our suggested new basis functions are the Fibonacci coefficient polynomials. We develop new theoretical results of these polynomials, such as their integer and fractional derivatives. The proposed approach efficiently estimates spatial and temporal derivatives using the operational matrices (OMs) of derivatives of the introduced polynomials. The approach converts the TFKSE controlled by their conditions into a non-linear system of equations that may be handled numerically. A thorough error and convergence analysis study for the proposed Fibonacci coefficient expansion is presented. Several illustrative numerical examples, including those with known exact solutions, are presented to confirm the efficiency and applicability of the suggested approach, even with fewer terms of basis functions. In addition, comparisons with some numerical methods are presented to verify our numerical approach's high accuracy.

Source: AIMS Mathematics

DOI: 10.3934/math.2025805

Authors: Waleed Mohamed Abd-Elhameed, Ahmed H. Al-Mehmadi, Naher Mohammed A. Alsafri, Omar Mazen Alqubori, Mohamed Adel, Ahmed Gamal Atta

Institutions: Cairo University, University of Jeddah, Islamic University of Madinah, Ain Shams University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funder: Islamic University of Madinah