An RBF-FD method for the time-fractional advection–dispersion equation with nonlinear source term

Londoño, Mauricio A.; Giraldo, Ramón; Rodríguez‐Cortés, Francisco J.

doi:10.1016/j.enganabound.2023.03.014

Engineering Analysis with Boundary Elements

2023

DOI: 10.1016/j.enganabound.2023.03.014

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An RBF-FD method for the time-fractional advection–dispersion equation with nonlinear source term

Mauricio A. Londoño

Ramón Giraldo

Francisco J. Rodríguez‐Cortés

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2024

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Cited by 3 publications

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Enhanced spectral collocation Gegenbauer approach for the time‐fractional Fisher equation

Atta,

Youssri

2024

Math Methods in App Sciences

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In this study, we utilize a specific combination of orthogonal Gegenbauer polynomials as basis functions that satisfy homogeneous boundary conditions in the spatial variable and homogeneous initial conditions in the temporal variable. We derive an expression for the fractional derivative of the temporal basis and another expression for the second‐order derivative of the spatial basis. Subsequently, we discretize the nonlinear Fisher problem using the spectral collocation method to transform the problem into the solution of a nonlinear system of algebraic equations. We then solve this resulting system using Newton's method with an initial guess approaching zero. Furthermore, we conduct an error analysis of the proposed method and assess its applicability through three test problems, providing comparisons for validation.

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Enhanced spectral collocation Gegenbauer approach for the time‐fractional Fisher equation

Atta,

Youssri

2024

Math Methods in App Sciences

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A novel local meshless collocation method with partial upwind scheme for solving convection-dominated diffusion problems

Zhang,

Lin,

Reutskiy

et al. 2024

Engineering with Computers

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A GFDM approach based on the finite pointset method for two-dimensional piezoelectric problems

Saucedo-Zendejo,

Medrano-Mendieta,

Nuñez-Briones

2024

Engineering Analysis with Boundary Elements

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An RBF-FD method for the time-fractional advection–dispersion equation with nonlinear source term

Cited by 3 publications

References 42 publications

Enhanced spectral collocation Gegenbauer approach for the time‐fractional Fisher equation

Enhanced spectral collocation Gegenbauer approach for the time‐fractional Fisher equation

A novel local meshless collocation method with partial upwind scheme for solving convection-dominated diffusion problems

A GFDM approach based on the finite pointset method for two-dimensional piezoelectric problems

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