Analysis of a fully discrete scheme based on the barycentric interpolation method for nonlinear fractional reaction-convection-diffusion equations

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Abstract

The primary objective of this study is to develop and analyze a numerical scheme to solve nonlinear fractional reaction-convection-diffusion equations, where the fractional derivative is interpreted in the Caputo sense. First, the nonlinear system is linearized using a direct linearization strategy, after which a barycentric rational interpolation method is employed to construct a fully discrete numerical scheme. A rigorous theoretical framework is established to demonstrate the stability and convergence of the proposed method. To corroborate the theoretical findings, several numerical experiments are conducted, illustrating the method’s accuracy, robustness, and computational efficiency. This work advances the numerical analysis of nonlinear systems characterized by fractional- order dynamics and provides effective computational tools to model complex processes in various scientific and engineering contexts.

Keywords

Caputo derivative / barycentric rational interpolation / reaction-convection-diffusion equation

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