Fractal-fractional advection–diffusion–reaction equations by Ritz approximation approach

• Main Authors: Md Nasrudin, Farah Suraya, Chang Phang, Chang Phang, Afshan Kanwal, Afshan Kanwal
• Format: Article
• Language: English
• Published: De Gruyter 2023
• Subjects: T Technology (General)
• Online Access: http://eprints.uthm.edu.my/9763/1/J15735_0a978ec0c88b43c83dfa97263e880111.pdf; http://eprints.uthm.edu.my/9763/; https://doi.org/10.1515/phys-2022-0221

In this work, we propose the Ritz approximation approach with a satisfier function to solve fractalfractional advection–diffusion–reaction equations. The approach reduces fractal-fractional advection–diffusion– reaction equations to a system of algebraic equations; hence, the system can be solved easily to obtain the numerical solution for fractal-fractional advection–diffusion–reaction equations. With only a few terms of two variables-shifted Legendre polynomials, this method is capable of providing high-accuracy solution for fractal-fractional advection–diffusion–reaction equations. Numerical examples show that this approach is comparable with the existing numerical method. The proposed approach can reduce the number of terms of polynomials needed for numerical simulation to obtain the solution for fractal-fractional advection–diffusion–reaction equations.