Ritz-Approximation Method for Solving Variable-Order Fractional Mobile-Immobile Advection-Dispersion Equations
نویسندگان
1 Department of Mathematics, University of Mazandaran, Babolsar, Iran.
2 Department of Mathematics, University of Mazandaran, Babolsar, Iran.
3 Department of Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran.
doi
10.30473/coam.2025.72692.1267چکیده
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.
