A SPECTRAL APPROACH FOR MULTI-DIMENSIONAL NON-LINEAR DISTRIBUTED CONVECTION-DIFFUSION EQUATIONS
Romanian Reports in Physics, vol.78, no.1, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 78 Issue: 1
- Publication Date: 2026
- Doi Number: 10.59277/romrepphys.2026.78.103
- Journal Name: Romanian Reports in Physics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
- Keywords: Caputo fractional derivative, Collocation method, Distributed fractional convection-diffusion equations, Romanovski–Jacobi polynomials
- Istanbul Gelisim University Affiliated: Yes
Abstract
This study presents a Romanovski–Jacobi (R-J) spectral collocation method for the numerical approximation of solutions to multi-dimensional non-linear distributed-order fractional convection-diffusion equations (DOFCDEs). Due to the inherent analytical intractability of such equations, the necessity for robust numerical approaches is underscored. The proposed method leverages the spectral efficiency of R-J polynomials to construct an accurate collocation scheme tailored for non-linear DOFCDEs. Emphasis is placed on the crucial role of advanced numerical computation in addressing complex phenomena governed by distributed-order fractional dynamics. The efficacy and accuracy of the proposed technique are validated through the successful resolution of four representative test problems, demonstrating its potential for reliable simulation and analysis of fractional systems.