Ritz-Approximation Method for Solving Variable-Order Fractional Mobile-Immobile Advection-Dispersion Equations

The advection-dispersion, variable-order differential equations have a vast application in fluid physics and energy systems. ‎In this study, ‎we propose a Ritz-approximation method using shifted Legendre polynomials to construct approximate numerical solutions for these equations‎. ‎The proposed method discretizes the original problem, converting it into a system of nonlinear algebraic equations that can be solved numerically at selected points‎. We discuss ‎the error characteristics of the proposed method‎. ‎For validation‎, ‎the presented examples are compared with exact solutions and with prior results. ‎The results indicate that the proposed method is highly effective‎.‎‎

کلیدواژه ها:

Caputo fractional derivative ، Mobile-immobile advection-dispersion ، Polynomial basis functions ، Time variable fractional order ، Satisfiers function