A Spectral Approach For Multi-Dimensional Non-Linear Distributed Convection-Diffusion Equations

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.